Whether you have sole or joint custody and you are the primary custodian or shared custody, unless your ex agrees to a written agreed order, you will need to get a court to allow it.
What do you need to show in order to make that happen?
First and Foremost that the move will benefit your kids and not just you.
1. The fact that you are moving to marry someone else could definitely work in your favor. The courts like to encourage cohesive family units.
2. Do your research! You should be able to show that the schools are better in the region where you would like to move them.
3. The court will also consider the fact that if your quality of life is improved, your kids will derive an indirect benefit. If you are making more money, they will presumably have a better quality of life.
4. Access to Extended Family is likewise important. You may not be allowed to move the kids out of state if the move will cut them off from their grandparents or cousins with whom they have frequent contact or maybe the move will be greatly beneficial for the children because they will have far greater access to extended family. Maybe that extended family will be able to provide the support and day care necessary for you to return to school and get a better job as a result of your increased education.
If you are contemplating a move, you will need to act quickly. Hiring an attorney sooner rather than later will help you get to court and could help you get a decision before for example the next school year starts!