Health,
The case has already been settled in a B”D. So the courts will usually defer to an Arbitrated agreement
(a psak B”D has this legal status because they coerce the women to sign an Arbitration agreement under the threat that she can never receive a Get if she does not sign. They also call it a “shtar berurin” and do not explain the legal ramifications of signing it)
The B”D ruled that the couple should share custody by alternating weekends and some weekdays. A special clause stipulated that Ms. Reich must raise the children religiously and that a beth-din-appointed therapist shall evaluate her periodically to ensure conformity with this clause.
What the husband is trying to do is find her in violation of the religious clause and and take away the days she currently has with her children.