Writing about psychological abuse is not going to be easy. As someone who is with someone who's previous was psychologically and physically abusive, it's a state of mind. It's something you have to feel and experience to understand.
Watch someone who has endured a decade of abuse and learn their ins and outs, understand that even something as simple as looking at them, even in a loving way, could cause them to go into an anxiety attack if you look too long.
Abuse means that they believe this person to be in control through fear. It means they believe they are worthless to anyone but this abuser. It means that even though the front door is wide open to escape, they believe and are convinced that the second they walk through it, there is nothing they can do in the world and that the abuser will find them, torture them, and bring them back.
To be unbroken from abuse while... not impossible, is not... likely. You can be defiant... for a time. You can be mentally able to endure the verbal lashing... for a while. If it's her father, this abusive behavior is all she knows and would not particularly be "resistant" to it because it is all she knows. Would something feel off? Of course, but it would be rationalized to well every family has their issues or it's just his way of showing he cares. There are going to be deep rooted issues that may not come to surface until someone else comes and hits a trigger.
Until someone shows them the light, the truth, until a kind hand gently touches them and pushes them out the door and says you have nothing to be afraid of or that this situation is very wrong, this life is going to seem normal.
Your idea isn't bad, but it needs more research. A human mental state cannot endure 10+ years (especially if MC is a teenager and the abuser is the dad) of abuse without being broken. There are going to be trust issues with men. Someone like a Father who is one of the most important roles to children and daughters, broke their trust, and will. There is a reason that people have "Daddy Issues". It isn't as light of a joke as people like to toss it around.
You would be better off having the MC girl be in a state of ignorance, followed by realization of abuse through an outside means (supporting character), followed by the struggle of breaking the abusive control and spending 90% of that time failing (for those of you who don't know, on average it takes someone being abused at least 2-3 attempts to leave an abusive situation), followed by her coping being out of a stressful situation (there is a huge emotional and physical shock once leaving a stressful environment full of abuse), and then dealing with the shortcomings of triggers from abuse from trust issues to trying to regain her life, her dignity, to feel like they are human again.
In the end there is no such thing as being unbroken from abuse. Even at the most mild levels, it still leaves a stain on our soul. Someone may not be fully broken in every aspect of their life, but something, some part of them did break and will break.
I will leave you with a quote she told me when she first met me, describing what simply meeting me meant to her:
I was stuck in a dark caged room [that was my mind]. Afraid and counting down the days until I die. Thought about even killing myself. I had given up, to just accept my fate that this was the life meant for me. I was in a room with no walls, no doors, no way out, and I felt trapped. Then you came along, and you gently put your hand to my face and turned my head slowly, gently to a wall I have never seen before. This wall had a door and a window. The door was opening and through that door, through that window, I could see the green meadows. You showed me another way, that life doesn't have to be this way.