Two of my characters don't really like each other for a while in my story, but after a while, they will somehow grow to like and even love each other. One of the characters, specifically, has had a pretty tough life and was abandoned by his parents, so he has a hard time trusting people. I just don't really know how emotions work in this situation, or how long it would take for him to go from not liking her to being friends to realizing he has feelings for her. Also how hard it would be for someone like him who has been emotionally and mentally manipulated and abused for a good portion of his life begin to trust her and eventually go so far as love her.
Begrudging respect is usually the place where feelings between two people begin to change. Often, it helps to have the characters go through something traumatizing together (i.e Harry, Ron, and Hermione fending off the Troll in the girls lavetory). Having the characters find small, endearing qualities in each other also helps advance the 'liking each other' process. Having one character take care of the other character, in a Florence Nightingale way, can also create an emotional bond that wasn't previously forged between them before. Having one character save something the other character cares about, for instance – have the boy be nice to the girl's little sibling, despite the fact that he doesn't like the girl herself very much. Or having the girl show kindness to the boy's pet, etc–allowing the characters to 'peel the onion' as it were, finding the depth of the personality beneath. Hope that helps!!
Maybe you could reveal some details the protagonist(s) notice suddenly that they are used to by now, or make the protagonist(s) think the "what if they/she/he were here?" scenarios. Then the reader will understand they are starting to like and care about each other.
Also, often you don't realize how much you enjoy a person's company, until they aren't there anymore. The old "You don't realize what you have until it's gone" scenario. :)
Sudden act of selflessness
I think an important thing is to avoid having mutual affection blossom out of abuse itself (though from the sound of it, it doesn't seem like that's what you're aiming for!). Often characters with troublesome lives with impose their negativity or cynicism onto other people, and that might lead to conflict. With such a hard past, there's likely to be times where a tough exterior vanishes and shows vulnerabilities that would undoubtedly be there in that sort of situation. A relationship that may be based off mutual bickering may soften when one character realizes that the other isn't as insufferable as they once thought them to be.
Perhaps the characters are forced into a situation where they might need to be together for prolonged periods of time and get to know each to a point where they understand the depth of each other's personalities? I know that in high school, there was a kid who frequently undermined me and annoyed me, but after being in the same group at school for a while we found things we could bond over and we eventually became friends. It doesn't have to be SUPER dramatic or emotional; sometimes simply getting to know someone can overcome the initial feelings you have for someone.
As for falling in love, some people take longer to realize attraction than others. Perhaps the character can find himself staring at the other (and potentially be caught!). Her kindness may prompt somewhat of a dependence on her, and whether it's a healthy level of dependence (healthy being desiring their presence in tough situations, whereas unhealthy would be needing her presence to feel ANY sort of happiness).
As for abuse and trust, many people handle abusive situations differently. Some people swear they won't trust another person because of what they endured, while other people put their trust in others too quickly with the hopes that someone will be able to "save" them. The latter sort of people might easily become vulnerable to other sorts of abuse, or they might luckily find someone willing to protect them and teach them how to escape the abuse they receive. The former, however, might frequently question the feelings or sincerity of the person who claims to "love" them and might look out for any signs of dishonesty. It varies depending on how they handle despair and stress!
OMG this is a great question!
I'm thinking Person A is super dominant, rude, annoying, outgoing, you name it. Person B is the exact opposite; quiet, respectful, introverted, right? Person A sits next to Person B in class or behind them in class or something and everyday Person A calls them something, touches them, or something annoying like that. Person B is super annoyed. Then one day Person A sits down and doesn't do it. They apologize to Person B for being like that, and Person B is like "no it's ok, I don't really mind it and I kinda enjoy it lol haha" and Person A is like "oh did not expect that" and then things amp up and they are dating, and Person A always does that "thing" to Person B but now instead of hatred its a sign of love and affection
sighs lovingly
OMG this is a great question!
I'm thinking Person A is super dominant, rude, annoying, outgoing, you name it. Person B is the exact opposite; quiet, respectful, introverted, right? Person A sits next to Person B in class or behind them in class or something and everyday Person A calls them something, touches them, or something annoying like that. Person B is super annoyed. Then one day Person A sits down and doesn't do it. They apologize to Person B for being like that, and Person B is like "no it's ok, I don't really mind it and I kinda enjoy it lol haha" and Person A is like "oh did not expect that" and then things amp up and they are dating, and Person A always does that "thing" to Person B but now instead of hatred its a sign of love and affection
* *sighs lovingly* *
I think one of the big things in a story of hate to love is that it doesn't happen all at once. You say that one of the characters has a hard time trusting people so it wouldn't make sense for them to just instentally realize they have fallen in love. Try placing them in a position where they have to be around each other and work together. Also, it helps if you place the character that struggles with trusting people in a place where they are comfortable (beach, specific diner, library, etc.) People don't fall in love with someone who they hate, so they should have at least a small friendship before either starts to realize that they are falling in love. Find things they have in common or find middle ground. This will help create a bridge between hate and love.
There a plenty of ways to go about it and you can use several of them. As was previously mentioned, your characters going through some sort of trial or traumatising event where they can get to know each other, and learn more about each other than their surface appearance. what helps is if the things they learn show that the two characters aren't quite so different after all. Sometimes you don't even need to have the 'liking each other' stage. If you do it right, you can keep them bickering and squabbling right up until one of them is about to lose the other and they think 'oh sh*t i really care about this person.'