In my plot, there are these 2 characters who were originally close to each other. However, they had an argument and broke up. In the end of the book, though, they get back together again. What I need help is for smooth transitions in their relationship. Every time I try to write it out, the flow of the story gets broken and confusing.
On-again/off-again relationships don't usually have smooth transitions. Especially not for outside observers (and often not for the participants). Add in that this is a teen relationship, and forget about smooth.
Since the relationship is not central to the plot, your narrative can just describe status changes matter of fact and not linger on them. I mean, show the emotions and the problems they have working together while broken up and anything else that you wish to show. But don't explain too much.
Readers understand that relationships don't always have soft and gentle changes. More like a stick thrown into the wheels. People argue, they're upset for a while, they may or may not be able to be around each other, and then, sometimes all of a sudden, everything's cool again.
Some couples talk it out. Some kiss it out. Others slowly hang out more and resume doing relationship things, so there's no clear point where the status changed back. Others just say "we cool?" and then they are.
Breakups are even more volatile. They can happen in under a minute. Or the anger and resentment can build up over time and then the break up happens after a long talk, or with yet another quick argument. Or people can drift apart.
Just give enough tidbits for your reader to figure it out and don't dwell on it.
If the work were about the relationship that would be different. But in this case, the relationship is background information and describing it has been slowing down your narrative.
If they are teens, I'd suggest you make the breakup a clear fault in one of the characters; preferably the more main character. By "clear fault" I mean one that most readers will agree with; a wrong-headed assumption of youth about "proper roles" or something like that; and something that with time the flawed character can overcome.
Hence making the flawed character the more main character; so you can show that personal growth. You don't need to show as much for the character that was in the right.
Then, follow the "try, try and try again" formula. As an example, I create Brittney as the main (flawed) character, and Alice (in the right); they are in love. They get into an argument over some principle Alice holds dear (religion, politics, reproductive rights, any hot-button issue you feel you can write about), and Brittney gets angry, Alice gets angry back, and they break up.
Alice (in the right) tries to get back together with Brittney because she misses her, but Brittney gloats that Alice came back to her and threw her principles aside. Alice doesn't want to be in that relationship, so End of Try 1.
Then Brittney, eventually sad at the loss, realizes she was wrong to gloat, and tries to get back together with Alice, but Britt won't admit she was wrong on the original point. Alice feels like this is all going to just repeat, so ... End of Try 2.
After enough time, Alice decides she doesn't care. She still loves Brittney, and she thinks she will just put her principles aside to be with the girl she loves, and will avoid the disagreement that broke them up in the first place. She comes to beg Brittney if they can reach détente for the sake of love, only to find out Brittney has changed and admits she was wrong, that Alice was always in her head, and she had seen first hand how wrong she was, but thought it was too late -- but if it isn't too late-- They kiss and make up.
You can, of course, make up your own reasons to break up, fail to get back together once, then twice, and then succeed on the third try. This is just the basic arc you can use to keep the relationship alive in the reader's mind, over the course of a long breakup. And in this time, the girls can have other romantic relationships that, in the reader's mind, threaten the Alice-Brittney prospects. Or make Alice or Brittney jealous and feel like they've lost their true love to somebody else. So the reader is relieved when these flings come to an end; it revives the Alice-Brittney true love possibilities.
This also doesn't have to be the main plot of your story; it can be sub-plot.
I suggest breaking the story into smaller scenes which you approach individually one at a time. Make each scene a connection between the characters that grows slowly over time, each scene bringing them that little bit closer.
Perhaps, at first, they are invited to the same party but refuse to speak to each other. Then something happens, an external event, that forces them to say just a few words.
Later, when they see each other again, the ice is broken. They are able to say a little more to each other, perhaps another event forces them to talk about what happened at the party.
On and on you go, each encounter, each external force, motivating them to come a little closer. That way, you keep the flow and it's not jarring, but believable.
One of my favourite examples of two characters coming together in spite of the odds against them is Eleanor Oliphant is Completely Fine. It's a fantastic example of character development and motivation.