You would seriously have to ask a lawyer.
From a laypersons understanding, and I am not saying I am right on all counts, but I the criteria would include: 1. The mother is a convicted felon on drug charges, in particular. 2. The mother is mentally unstable. 3. The mother consents to the father having primary custody.
Otherwise, the default is the mother gets primary custody, but cannot deny the father time, or that is punishable by law. Even if the father owes support…
Sadly, TOO many people I have known go through this spin cycle. Its tragic.
In cases where the mother is very difficult in allowing the father time with the child(ren), usually after some time the moms ending calling up the fathers to take the kids as much as they can get away with.
Rabbi Noach Weinberg Zatzal, olav hashalom, said something to the effect, “Three out of five couples who say, I do, end up saying, I dont. And who knows what is going on in the other two marriages?”
I am not sure why you ask your question, but I hope no one has to deal with this, and if they do, I hope it works out for the better, rather than the worse.