Why not just stick with telling them about the issues around drink first. For a start off it might help them to not drink around you or be wondering why you're not drinking (adding 2 and 2 and coming up with 5).
If you do decide to tell your mum about the assault, be careful that you don't give the impression that the drinking is because of the assault, as this could confuse matters. Actually, from what you've said, that isn't really the case.
Also, be wary if having any expectations about how either of them will react. You may not even see much of a reaction as they're likely to need some processing time. You've had a while to get your head around all this and still find it confusing, so don't be hurt or angry if they need some time and space to process it as well.
I think it's great that you want to involve your parents in your recovery and resolve to live a happy and sober life. You might want to keep the other side of things to a general statement that you've realised that getting so drunk has put you in some dangerous situations which you don't want to risk being in again. That can then open the conversation up further if you want, or not for the moment, but they're likely to be able to imagine the kind of thing you mean.
Try to keep things at least a little but simple for today. No doubt you're feeling extremely ropey. Bless you. Xx