Kurt,
The whole situation here and how you feel about it comes down to this sentence of yours:
I really just wish that she would come back and forgive me.
Let's look at the facts here. You gave your mother a letter telling her who abused you when you were younger. She disbelieved you and thought you were making it up to get attention. She even showed the letter to the abuser, whom she likes, and the two of them made fun of you. Then she sent you to go work with that very same man on the repair of your house, even though you protested and told her you didn't want to go. While you were working with him, that guy, an adult in his late 20s who outweighs you by over 100 pounds, beat you up and put you in the hospital. When you came home, to your Dad's place where you and your mother were staying because of the hurricane, your mother had to take care of you but did so with not much enthusiasm. Then finally she took off, as you describe in your post.
Maybe I am missing something here, but I don't see ANYTHING that you should feel guilty about. You don't need to be forgiven. You have done nothing wrong.
What's totally clear is that your mother is a very poor parent. It's outrageous that she disbelieved you; it's incredible that she showed your letter to the abuser; and it just staggers the imagination that she would pressure you so badly that finally you agreed to go work with him.
When this whole thing ended with you being so terribly hurt, I imagine she felt very guilty about how badly she had handled things. But on second thought, perhaps not. Perhaps she has emotional issues of her own and just doesn't see what's going on here. Perhaps she just doesn't understand her responsibility as a mother.
I'm not trying to run down your Mom. I know how you feel about her and that's fine. It's natural for a teenager to love his mother and want her love in return.
But frankly speaking, I think you are best off exactly where you are now - with your Dad. It isn't your job or your responsibility to fix things with your Mom. She is the adult here, not you. She is the one who moved out and left you, and she is the one who has broken off communication with you.
There is nothing here that you can fix, Kurt. She is going to have to sort out her own problems and decide whether she can be a real mother. It's possible that she can't do that now. Will she be able to do this in the future? Who knows.
But the really essential fact here is, again, that you did nothing wrong and don't need to be forgiven. Through all these months I think you have been very brave; you have done exactly what you needed to do. Unfortunately, at every step she has failed you. But remember, that is her doing, not yours.
Much love,
Larry