It really depends on your state as I have learned. My state has a pretty much mandatory 50/50 custody arrangement (how anyone thinks that's good and stable for young kids I have no idea) unless the other parent is in jail essentially.
I am not backing down on the request (my lawyer is dealing with it, not me) that there be stipulations about what to do in the event I even THINK he is drinking while with the girls (if I speak to him or get a call from D6 suggesting something is up)...
He isn't arguing the stipulation part as far as I know which I find interesting.
Anyway, I'd suggest finding out first what the status quo custody arrangement is in your state bc it seems at least in mine that is where things start and then you have to argue why there should be changes to it from there.