I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that the mother is doing this.
It's not against the law for the children to spend time with you when their father is away. If the court order gave the mother a right of first refusal over babysitters, that arguably would mean that the father would have to get her permission before leaving the child with you. However, for one thing, that sometimes only gives first refusal for NON-family members, and your now a family member. But also, if that's there, your husband can file a Motion to Modify Custody, asking the judge to make it explicit that he can leave the children with you before getting consent from the mother.
The father has a right to allow the children to stay with you or other relatives during his regular parenting time unless the court order says otherwise, and it's not for the mother to decide. It's the father's choice. He has the ability to file for contempt as soon as she doesn't deliver the child, but it may help to file the request for modification at the same time (or first), so your husband can get a clear ruling at the same time he files for contempt. The benefit of doing it that way is, then you have a very clear court order where she's obviously in contempt if she doesn't bring the child over. Now, where the order doesn't explicitly require the mother to give the son to you, it's possible a judge would say she's not in contempt (although I still think she is).
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