So, I have a character who was going to just be an unlikable character at the start of the novel, but now I want to make her more caring towards certain people, like the innocent character. Thing is, I also don't want to go overboard all over again. I want to balance her character between tough love, and being a complete ass. she needs to be disliked, still, but you can also see that she's redeemable with character development. But how do I do that?
Look at her motives.
"Tough love" is someone making hard calls or asking difficult things for the right reasons. A parent making you get up at 6:00 a.m. to go to school no matter how tired you are, or insisting that you do all your chores before going out, because it teaches you responsibility. A drill instructor who goads trainees to finish a grueling obstacle course because it teaches endurance, perserverance, and a belief in yourself.
"Being an asshole" is someone being mean to you for the wrong reason, or no reason, or because the person enjoys being cruel. Making you get up at 6:00 a.m. on a weekend just so the person can berate you for not having a job, or making you scrub the toilet with a toothbrush. A drill instructor who makes you do pushups in the rain for hours because your bed wasn't made to the nth degree of precision. Bullying someone for being fat.
Particularly with someone like a drill instructor, there can be a fine line between tough love and bullying, so your reader should see that your character means well but may be overdoing it and not realizing it. So you show that your character can be nice to someone who doesn't require instruction (doesn't have to be "someone who's innocent"), and that can open the door to character development and growth.
First of all, forget what the readers and characters think, or are supposed to think, about your Tough Love. Instead, think about what you want for it.
I think it's very easy for someone to see a tough character as an asshole, and it's tempting to paint an asshole as representing 'toughness'. Notice that 'tough love' is usually how a tough character supposedly expresses their feeling of caring so, more than 'tough love', I suggest focusing on 'tough' in general.
I'm going to paint a scenario for a tough female character and I will do it from her POV. Then we can translate it to what the others are seeing.
personal view on life
TC is a grown woman in her twenties. Even though she's young, she has no illusions about the harshness of life. She has either lived through hard times or seen her loved ones live through hard times. She does not think of herself as negative, but as 'realist'. In fact, she's an optimist since she does belief that taking action can (though, life being life, it's never guaranteed) make changes for the better. Or the worse: just because you have good intentions and work hard in accordance to a sensible plan of action, it doesn't mean it won't blow in your face through no fault of yours.
personal view on others
TC dismisses anyone who gets carried away by their idealised dreams. If it turns out to be a grown person, 'dismissiveness' will likely become 'disgust' and she will have a hard time hiding it. A child will merit a sigh and a 'you'll grow up and have your dreams and hopes squashed - better get used to the idea'.
And that is precisely what guides her interactions with younger people. She knows teenagers have ideals and will get carried away by them. The sooner someones burst their bubble and makes them see the stark reality, the better for them, as they'll suffer less heartache. It's a kindness, really. Not that she is interested in doing it herself. They're none of her concern. But she will look over them, shaking her head, waiting for the crushing blow. And then she will stand beside them and give them the example: get up and be smarter.
As for older people... there's no worse blind than the one who refuses to see. If they insist in being stupid, then by all means, she will either let them know how wrong they are and how stupid they are to persist in it, or she will shrug at them with contempt. They're much too old to believe in pink unicorns!
caring for people her age
TC has a soft spot for Cheerful. He's a great guy and he'll help anyone who needs it. He's always smiling and has a positivity that spreads like the flu. One has to respect the way hardship will not put him down: he just keeps going. But he's heading for heartbreak. TC can see it clearly so she will tell him so in no uncertain words with her best advice.
TC also has a soft spot for Capable. He's strong and he's overcome his share of heartbrake, so she has all the respect in the world for him. To show it, she makes sure to comment his decisions, pointing out what she thinks is good... and pointing out potential problems. She has no intention to nag or belittle, quite the opposite. To pat him on the back for a less wise decision would be to mock him. And if he does fall, she will be there ready to upbraid him and get him back on his feet and in the right direction. He deserves no less from all his done.
caring for a younger person
TC has a soft spot for Naïve. He's full of dreams (appropriate to his age) but he's woefully unprepared and ignorant on the ways of the world. TC will make sure to get him aside and open his eyes. Since he's much to engrossed in those hazy ideals, she'll be blunt. She may even be purposefully cruel. Better to receive a control blow that will set him straight, than to be completely smashed by the world.
caring for an older person
TC has a soft spot for Weary. He's had a long life full of trouble and he's pulled through as best he could. Now, though, he's old and out of touch with reality. She will stand behind him, ready to catch his fall and she will do her best to kindly protect him and guide him.
She will do her best to be kind to those she cares for. However, she has no habit of sweet, soft words. Life has always been rough and direct with her, and she has learnt that lesson well.
Some people may call her rude and iron fist, they may say she's an asshole and a jerk. Let them! She knows that her approach is the best way to go through life. If people get all shocked and appaled, that's because they grew up in over-protected bubbles of fluff. She ignores them. After all, that view on life will get them hurt, not her.
This is a rather long example, but it gives the general idea. Your character does not think of herself as an asshole. Give her a good reason for her way of being and acting, and let her believe she is living life right. It's the others who are oh-so-sensitive.
In the meantime, the other characters don't as much as suspect she means well when she tells them to stop whining like a baby, or insists that they repeat the same task over and over when it has already been satisfactorily done. They don't know she simply wants them to improve and excel.
Tough Love characters are tricky to write and can cross from loving but strict to abusive pretty quickly. Consider the family in Malcolm in the Middle, where Tough Love seems to drive the family more than anything (especially with Lois at the wheel). It's of course played as the ultimate dysfunctional family for humor, but there are some very sincere moments where the behavior is understood for the love motivating it (One of my favorites is "Family Behavior" where the full fury of the clan is unleashed on paternal extended family after their out right abuse of Lois. It even ends with Lois acting as a better person when she realizes she was starting to morph into her in-laws. And multiple episodes show that despite Francis' and Lois' open contempt for each other actually did help Francis mature and become a decent human being.).
Here the key dynamic was that the series took every opportunity to make it very apparent this wasn't motivated out of malice but because they knew exactly where the line was AND it was all internal to the immediate household. Most of the best moments are shown to occur when one member is attacked by an outsider who is plain abusive.
For a softer "version" we have Bruce Wayne from Batman Beyond, where he is now the mentor to the new Batman, Terry and also a very crotchety old man who can still kick ass, even if he needs a cane to walk. In this case, it's pretty clear that Bruce does care for Terry's well being and wants to help as much as possible, and Terry is clearly taking the mentor-ship seriously, but they were both stubborn and butted heads. One of the most praised episodes, which sees the return of Mr. Freeze, draws much of the conflict between the two from their opinions on the villain's supposed reformation, and comes to the conclusion that both were correct. It's also shown that the two are different in style, with Terry being less of the detective than Bruce but was more charismatic and able to get into peoples heads without fear, most notably realizing that while Bruce didn't listen to the Joker, something which Terry is less able to do, the Joker always wanted Batman to laugh with him... but not at him.
Some other things that are common in this trope is that the Tough Love mentor doesn't teach by giving you answers for you to regurgitate but instead teaches to find the solution on your own. They often tend to be older and realize their own mortality. They tend to favor creativity in their student's solutions and are best paired with students who do not recognize this quality in themselves. Consider the Sword Master from the Avatar: The Last Airbender episode "Sokka's Master". Contrasting the sadistic nature of the family in Malcolm and the gruff exterior of Bruce, here the Master is rather calm and more eccentric. He is vague on what the lessons are supposed to teach Sokka about Sword Fighting and why painting, rock gardening, and calligraphy are on the list of things to know when learning sword fighting. And he openly admits that Sokka wasn't the best student in these tasks... but the point was that in every task, Sokka to a very unique approach and thought outside of the box... The only time he comes off as abusive was when Sokka admits he's from an enemy nation to the master's but even here, where he lays in with an actual sword fight, its still a lesson and the Master, upon winning, admits he knew the entire time, and this was more a final test to see how Sokka would handle himself in an actual combat scenario. One of the key features here, is that the characteristics that he's praising Sokka with are not unknown qualities to them at this point... Sokka was long known to the audience to be honest, creative, and able to see angles others were not able to see. What the Master's lessons did help him to see the advantage of these qualities in combat.
Tough Love requires Love. Bullying requires a disregard of the feelings or dignity of the victim; or even getting satisfaction out of causing pain, humiliation and distress.
However, I'm gathering you want her to be disliked but also redeemable: That is possible without resorting to "tough love."
First, she can be disliked without being hated, and without being a physical bully. She can be intentionally mean, disdainful or insulting, for example. I don't know your setting, but an example is somebody informing the group of winning an award, and she responds "Congratulations, you made a hundred people unhappy doing it", or insults them or claims she thinks they are lying about it or cheated to get it.
Her flaw is that she is unhappy with her life in general, and other people's happiness feels unfair to her, they don't deserve happiness if she doesn't get any. She feels like they are cheating somehow, taking more than their share, making others unhappy so they can feel happy, and her insults (subconsciously to her) are a way of punishing them for taking something she doesn't know how to get.
But notice that flaw doesn't really apply to somebody else that isn't getting any happiness. If she thinks the innocent person is unfairly denied happiness like SHE is, then the innocent isn't guilty of "being happy." And in that case, your disliked character may have sympathy for somebody in the same boat as she is in, and she can do something about it: she can be kind and sympathetic, and because she knows she is voluntarily providing any happiness that creates, she doesn't feel like the innocent stole happiness or took it at someone else's expense, she knows it was given freely because she gave it.
If you want, that can become a mutual ongoing exchange; the innocent can return the favor, and your disliked character could decide after some time to voluntarily extend a kindness to somebody else. she could doubt her assessment of them as "bad because they are happy", because she has learned that isn't always true, and sometimes giving away a kindness is how you make a friend, and friends can make you happy.
There is a character arc there, by the end of the story she might even apologize to somebody she insulted early on just because an apology is a kindness. She doesn't have to become a saint; but it would become clear she is on her way to stop being an ass.