There used to be a female judge in NYC who kept toothbrushes on her bench in a mug—for the guys who lost the case and had to go to Rikers Island. I think they do that only if the woman agrees to it, and I think she is gone now. Sued for assault maybe.
I would advocate a simple system. The wife specifies an amount for child support. The husband then decides whether to pay it, or take full custody.