My husband got fired from his job two weeks after he moved out. Each state's laws are different. You need to get a lawyer ASAP.
In my state (SC), you have equitable distribution of marital assets. This includes EVERYTHING that has been purchased, made, won, etc. during your marriage. It doesn't matter if YOU won it...it's included. Your winnings and your house equity will likely be included in your marital assets. I would NOT offer him any money until you get papers filed with an attorney. I personally would request child support from him. Just because you can support your daughter does not mean that he shouldn't, ya know? Think of that extra money (if you get it from him) as "gravy" money for the tight times. Actually that's what my plan is right now just so that I don't have to depend on his money (in case he doesn't get or can't keep a job).
I would report the incident last night. I agree with Hadenoughnow completely. Start keeping documentation of the drinking. Again, not sure of your state, but in SC, you can use alcohol abuse as grounds for divorce.
I know what you mean about wanting all of this to just be done, but divorce is a process which can take awhile. Right now you need to protect you and your daughter. You need to tell someone about what happened last night. It sounds like you feel embarrassed because you hit him first. Sure...it wasn't the smartest thing to do, but no way did you deserve to be hit like you described.
(((HUGS))) I was so scared when I first left, but honestly, every day since then has been a DREAM compared to the days that I was with my STBXAH.