The grammar is mostly good. I think he is probably used to understanding how you speak in English, and he must love it well enough, so rather than try to make it sound more native, I am only suggesting changes that correct things or make things more clear.
I’m not certain what you mean or imply by the first phrase “I didn’t want to reject you”. I think you might mean to say “I wasn’t rejecting you” or “I didn’t mean to seem like I was rejecting you”.
I don’t understand what you meant by “but of course soon I must”. As written, it means you will need to in the near future. So it would refer to something in the future, which would only seem to be leaving with your lover, but later you wrote you’re not at that point yet, so I think you probably made a mistake with the tense, and were talking about how you had to go home in the past. Assuming that’s right, I corrected it to “but of course I would have needed to return soon”.
The last sentence of the first paragraph seems to have the negative backwards.
I am not sure what you meant by “it’s hard to love one’s self when he’s alone” – is “he” your self, which is just a pronoun gender mistake or maybe it would be masculine in your native language (it would match your gender in English)? Or do I misunderstand? Should it be “it’s hard to love one’s self when I’m alone”? Or is “he” your father again, so you mean to say something else? I wouldn’t know what. I think that part needs more explanation unless it’s something you’ve talked about with the reader before that he would understand.
Here is a possible edit, though the bold parts I am not sure I understand and think you should make sure clearly say what you mean:
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I didn’t mean to seem like I was rejecting you when you asked me to leave with you. I know I wouldn’t want to go back if I went with you, but of course I would have needed to return soon. I was stuck. If he finds me gone; if he catches me sleeping over at someone else’s house, there would be black and blue. I don’t want to get hurt. He’s unpredictable. I’m only free when he’s not here. When he is, I have to walk on eggshells.
I apologise about the self-pity and impulsivity last night.
Life feels pretty hopeless recently and I’ve been dealing with a lot of self-issues in the past few months, mostly about my self-worth. I’m unstable. I have a lot of self-loving to do. I know you don’t like people who don’t love themselves, but it’s hard to love one’s self when [I’m?] alone. A storm is staying for a vacation, there are no silver linings yet but I hope they come soon.
You were right. Small things, big impact. I think I really missed something big. I should have followed my instincts. I wish I wasn’t so careless.
Forgive me for not coming with you. I’m sorry.
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For “I hope you ask me to leave with you again”, how about “I like the idea of leaving with you, in a way that would work well” or “let’s talk more about how it could work for me to leave”? Though I am also unsure if you mean to leave and stop living with your father, or just to find a time you can spend away with him without getting caught.