What to do if my children’s father is in jail and I applied for a custody hearing but the judge won’t give me full custody until he is out of jail?

You have a couple of different issues in your question.   The first is regarding the judge not allowing a hearing to go forward.  More than likely, the judge is concerned about violating the father's due process rights.  In New Hampshire, like most states, a judge has to afford both parties due process to participate.  If there is not a way to allow him to participate while in jail, he would have to reset until something could be arranged-- assuming dad wants to participate in the hearing.  Given this seems to be his issue with having a hearing, you can (1) wait and have the hearing after he gets out, (2) see if you can get the father to sign off on an agreed order while he is still in jail, or (3) dismiss the custody suit and refile your action later (assuming that you filed the motion or suit).  If you are merely a respondent in a custody suit, you would not be able to dismiss the suit.

The second part of your question is regarding movement to another state.  You mention that you are filing for full custody, but you did not specify whether or not some orders are already in place.   If there are orders in place and they do not restrict your right or ability to move, then you can move to another state without any issues.  Similarly, if there are no custody orders in place, then you can still move, because there is nothing to restrict your right to relocate with your child.  If there are orders and they do contain provisions that say you cannot move, then you would need to follow the orders-- or have them modified by the court so that you could relocate.

Before moving to another state with your minor child or children before there is a custody hearing as to the matter you have written about, I suggest that you consult with a family law attotnry as to your legal options and whether the intended move with your children could be in violation of an existing court order.