All my questions and a good deal of my concerns were quieted when I paid to see a lawyer. I saw someone who specialized in cases of domestic abuse and alcoholism. To her, my story was a dime a dozen, and she knew just what my worries were. The consult was 120$ for 2 hours, and it's the best money I've spent so far.
If you are separating from your AH, a similar kind of consult (there are also free phone consults) might be useful in settling your mind with regard to custody and visitation.
You may not like the supervised visitation route, but it may be necessary for a while. I don't know if the laws are similar where you live, but I was told that here, in Québec, visitation can always change depending on a change of situation. So you might start out with supervised visitation and then gradually move towards unsupervised and then perhaps later, equal shared custody.
If you're concerned, I'd go with that. A legal consult doesn't mean you're taking action right away; you're just getting info.