What happens if my divorce agreement states I can't move out-of-state the with children without permission from the father and he won't give it?

It is not a may, it is a must if you want to relocate. 

The test is the best interests of the child, and this could get complicated.

The answer is that the view is not required to agree.  he may have reasons for his reactions. 

The Court is not the place where the matter needs to be resolved.  If you move without the court's permission, this could cause major problems.

If you need assistance, contact me.

You have a right to go to court and seek a modification of the divorce agreement. If you have a legitimate reason for moving out of state, then I see no reason why the court would not allow you to move. Your ex-husband would need legal grounds for seeking full custody such as your children would be in an unhealthy situation living with you and your new husband. I don't know the facts of your case so I can't say if he could win or not on those grounds. But as long as your ex can see his children, and they will only be 30 minutes away, I see no reason for your ex to be unreasonable and uncooperative.