You are free to tell the father that you want to charge him a specified rate for taking care of the children during his parenting time. If he agrees to pay, then you can charge him the agreed rate. If he does not, then you can expect that he'll seek child care services elsewhere.
If you have something of which your daughter is not aware that you believe is relevant to her custody case, tell her about it. It's up to her, whether or not she does anything with that information.

