Thanks for the chance to help. I am an attorney with over 12 years experience. Hopefully I can help you with your legal question.
The one concern I would have, were I you, would be if your seemingly amicable divorce turns contested.
Since if the case turns contested, you would need to hire an attorney to protect your rights (and your right to the children)
Lets back up...a divorce can be either contested or uncontested
Uncontested; Now the fastest, (and by far the least expensive) way to get a divorce is if you can agree on the terms. If you can agree on "who gets what" there is not a need for attorneys...this will cut the costs to a very small amount (court fees)
Contested; if you can not agree, this is a contested divorce. To proceed you need an attorney or need to act as your own attorney (very bad idea). Here the parties present evidence to the court on "who gets what" (including custody of the kids) and the court decides. This take longer and involves attorney fees for both sides.
Now, for the kids, you have the Uniform Child Custody
Jurisdiction And Enforcement Act (UCCJEA). This is the law that will kick in to determine what court has jurisdiction over the kids. If the kids have lived in UT for the past 6 months, that state would arguably have jurisdiction. That would force the divorce to be filed in UT.
Now...there is the Service Members Civil Relief Act (SCRA) that allows a service member and their spouse to maintain their residence despite their military move...so if, for example, he kept his residence in some other state and filed in that state (and not UT), then it could be you bypass the UCCJEA...but this would be up to the court to decide (the law is not clear as to how the UCCJEA and the SCRA interact for a divorce filed outside the state where UCCJEA claims jurisdiction.
Basically....if you can agree on the terms of the divorce and "keep it friendly" this will not be an issue...since the court is going to work with you over custody of the kids. The court wants what is best for the kids....and if you both agree? Say you agree that once you settle, the kids live with you in NC? The court is not going to oppose that.
However, if this turns ugly and he begins to contest the divorce...that forces you and he to hire lawyers and the court then would be forced to decide who is best suited to have primary custody with the parents living in separate states.
Generally speaking, you still have an edge...if he is active military, particularly if he is subject to deployment, the court generally will favor primary custody with mom...but that is not set in stone. It turns into a fight in court as to who is better suited to raise the kids.
BotXXXXX XXXXXne: If the kids have lived in UT for the last 6 months and you or he file for divorce in the near future, UT has jurisdiction over both children (even the child who is with you currently in NC).
If you were to remain in NC for 6 months, then the child or children living with you in NC would fall under NC jurisdiction for UCCJEA purposes. So if your goal is to divorce and live in NC, you may want to see if you can get both children in NC for 6 months or more before you file.