Moving out of the city with custody agreement in place

We’ve had a custody agreement in place for right at 3 years. We have 50/50 joint legal and physical custody.
My children at 9 and 5.
Our marital residence was awarded to him in ED since he asked for it to be even though its currently in foreclosure.

He has recently stated that his plans are to move to Charlotte and live with a friend of his.
We live in Concord. My children both attend Cabarrus County schools.

Our custody agreement does not talk about where we have to live or what schools the children go to.
However, I assume since we have lived in Concord since we were married and my daughter has always gone to the same school, that he would have to petition the court to change that.

But my question is more this. He COULD move to Charlotte and still get the kids back and forth to school every day, but it would certainly not be in their best interest as they attend an early start school and would have to be up at 5:30a to get ready and leave in time to get to school.

Plus, my 9yr old daughter would be living in a house with a 42yr old single man who’s not her father.

Any rules around moving out of the current city if its not documented in the custody order?
Would his moving be considered drastic enough that I could file for emergency custody if he did that?

No, this is not going to be enough to file emergency custody. However, it might be enough to file for a modification due to your being uncomfortable with a man you do not know being a roommate with your ex and around your children, additionally the school issue. If you don’t get a modification, he will need to continue to make sure that the children get to their regular school (drive them there). Yes, they would have to get up extra early because of this. You must continue though with the 50/50 arrangement unless/until a modification is granted giving you primary custody. You can refuse to allow the visits if you feel that your children are in real danger or have been neglected. You may have enough with his move to file for a modificiation if these changes are sufficient to show a substantial change in circumstances has been created that negatively affects the best interests of the children.