Typically a parent only has to give notice the the other parent if they are moving within a state and taking the children with them. In this situation, since he is having his parents assume a temporary guardianship and is not taking the children with him, there would be no obligation for him to notify her as to his out of state job search. As long as he was leaving the children with a competent and capable caregiver, he can't be accused of any wrongdoing.
If he is able to secure employment in another state, he would have to notify his ex and file a petition with the court for the judge's permission to move. However, typically a job offer is considered reasonable grounds for a judge to allow a move, even over the objections of the other parent.
If he has executed a legal temporary guardianship leaving the children with you, then no, you would not have to give them to her unless it was her stated custody time. If it was her time, you would have to deliver them. As long as he has arranged for appropriate temporary custodians to watch the children while he is away, she has no legal rights to take them back.
Unless she gets a judge to agree with her and issue an order for you to release them, you would be under no obligation to do so.
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