I was terrified of going to court with my ex, but the truth is, he was really foolish and delusional to take it that far. If he had settled for any of our offers in mediation (mandatory in our state) rather than insisting on dragging it to trial, he would have gotten a much better (and cheaper) deal.
Asking for what you want- sole custody/supervised visits/whatever- is really just a matter of filing the papers, and the lawyer will do that. A trial may or may not happen. Lots of cases get settled before that. It sounds like your ah might not be in a position to really fight much, so you would have a good chance of settling in mediation or through your attorneys before a trial.
Ours was just custody, since we were not married and the child support issue was settled earlier in his home state, but I ended up getting everything I asked for and then some, so in the end it was worth it. In my case it was about protecting our son from his drinking behavior, since he got it in his head that he was entitled to shared custody, unsupervised visits and all kinds of other things. I could have saved myself a lot of trouble and expense if I had handled it sooner and not procrastinated. I initially had to pay out of pocket for a lawyer in his home state because he filed a case there first, so that had to get dismissed before I started legal proceedings here.