You didn't indicate what kind of parenting arrangements they have - is it equal time? Is he primary? Is she primary? If the mother agrees to allow the children to relocate with him, then they need to create a new long-distance parenting plan that specifies when and where she will see the children and how the travel will be handled. If she does not agree, then he can ask the court for permission to relocation. This is very difficult because he'd have to convince the court that it is in the children's best interests to live in Texas. If she does not agree and the court will not grant him permission to relocate with them, then he might want to consider negotiating with her for a long distance plan if he joins you in TX and the children remain in AZ.
** This response is provided as general information only and does not constitute legal advice or otherwise establish an attorney-client relationship. **
The relocation statute provides some rules you have to abide by in order to even try and locate. If they have equal parenting time then he cannot move the child without the mother's agreement or a court order after a final evidentiary hearing. If he is primary parent then he might be able to move on a temporary basis if he is leaving for a new job, health safety or welfare of him or the child. However he MUST follow the procedures of the rule 25-408 or he could face sanctions of the court. I would suggest he consult with a lawyer before doing anything.
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