How to start fixing problems with my mom?

There's so much to say and so little time. Well to make a long story short, my childhood was not the greatest. My parents were separated and there was a lot of alcohol abuse with both of my parents (and they did not get along well) and my brother physically abused me. Well when i was younger I had always felt that most of this was my mothers fault and my mother had a new man in her life who was number 1 and i was always put after him. That obviously created a very messed up relationship with my mom. I had severe anger problems through ages 12-16 and I remember just telling my mom I hated her all the time because i was SO angry. If i wasn't angry I was crying. I had to go on anxiety and depression meds and into therapy to get my emotions under control. In therapy a lot of stuff came up that pretty much had to do with my mother and so the therapist said we had to try to find the root of the problems. Well we did that and I do find now that I am not that angry person i was then and my mom and i DO have a better relationship now but I catch myself from time to time (especially when im upset with her) I get that anger back. I don't mean to, it just happens and after Ive spoken to her I feel awful. Then recently some things about the past have been brought up and i realized when i was about 14 (i am 24 now) i did something to my mother that I feel AWFUL about now. At the time I didn't think twice about it or her feelings but now knowing how her she was is KILLING ME. I feel like I am the worst child. I cant even think about it without crying. My mom says she forgives me for everything (which I do believe her) because she can understand how easily bad things can happen to you or change you. Shes so understanding which is what kills me more. I just want to make up to her all of the bad things I did. First I want to know why it is i find myself treating her like that? Shes very good to me now and i just catch myself giving her the attitude before its too late to take back. I am just looking for tips/guidance to anyone who has had a difficult relationship with their mother. How do you try to fix things when all the bad things are still somewhere deep inside? Therapy is not an option, we dont live close enough and dont have the same work schedules so it would be very difficult.

I appreciate any advice, tips, guidance!

I should probably also mention I didnt have a great relationship with my dad either and he passed away unexpectedly I am also full of regret for not fixing things with him. That is probably why things with my mother are much more emotional now.