Can I move out of state with my 2 children even if the father disagrees, we don't have any agreements through court, I'm in New Hampshire?

You are taking a risk by moving without consent from the court or your ex.  If you move without consent, the court may order the children to be returned to NH.  If the children return to NH without you then your ex will likely get custody.  If you petition the court for permission to move, the court will decide if you are moving for a legitimate reason.  Then the court will decide whether it is in the best interest of the children to relocate out of state with you or stay in NH with you. Best wishes