Can my ex stop us from moving to another state?

He cannot stop you from moving, but he can go back to the Family Court and request a change to the previous orders. The only thing he can do is request that he have primary custody instead of you. It sounds highly unlikely that he'd win that, given the previous orders. Obviously, your 19 year is is no longer subject to the court's visitation schedule, and at 17 years old, that child would get to choose who he/she wants to live with. The 13 year old would probably get to have some say (if he/she wanted to express an opinion), but given that you have sole custody, the court would be very unlikely to suddenly give their father primary custody.

You need Court approval to relocate the kids. You need to provide a lot more information to get an informed prediction of the outcome. You will lose as long as, like here, you give no substantial reason for moving.

The father can file a Request to change custody alleging that the move is detrimental to the children and that the best interests are they continue to live in their current state. An attorney can help evaluate your Judgment to determine whether you need to request permission from a Judge to move or if you merely have to give notice of the move.