If the court order doesn’t force her to stay in NH, leave, leave in 10 minutes.
The father will then lose the ability to see her unless he follows. Or can future Nazi state court order cross state lines.
When my husbands case went before the judge (he has a daughter from a high school hussy) that judge made it perfectly clear to both of them that no matter where either of them moved to he (the judge) maintained complete court authority over the case.