Excuse me for answering a question with a question, but are you asking this for yourself? Surprising, I ask why a casual game has no black people and my question is removed, you ask if it's legal to abduct your kids, and that seems like a good, clean discussion to the mods.
In cases where custody is not established & both parents are presumed "responsible parents," the right to possession of the children can be challenging without the establishment of legal determination (i.e., sole legal and/or physical custody, shared custody) No parent has the right to restrict access of the children to the other parent without "real" cause;which, by the way, is best established inside the court system (or so we believe). Depending upon your actual circumstances, there are several potential ugly words that go along with the scenario you have provided: abandonment, kidnap, abuse, and the litany goes on. It's not good for the children, they most assuredly don't understand the debauchery of grownups, nor do grownups understand the damaging emotional/financial pain caused to the children who believe they cannot speak in the midst of the heat of what is going on between the two of you. Be careful of what you allow the court system to do in your behalf, especially if you or your mate are angry -- anger never solved anything, keep that in mind.