How old are the children?
You would have to gain custody of children on school days in order to register them in your district or half half custody.
You prob will not win this in court as you are not in current school district so the kids will have to move districts anyway.
Is there a reason she is moving to that town? Did she buy a house already?
You can always suggest that they move to your school district and do half custody where she can drive them to your district on her days and split the week, or do one week you, one week her. This would prob only work if you both can agree to it as it takes co-parenting to do this and a judge will prob not just do it.
Send her an email, something like this?
Ex,
After hearing about the kid move, I agree they should stay in xx schools until the end of this year. I am willing to help with the driving if needed. As for next year, would it be possible for them to sign up here at xx district and we can split custody. XX district has more to offer and a better school district. I would be willing to do some driving on your days to make it easier. We can work out a shared plan. (You can suggest that this will not affect
child support as she may not go for it if she thinks you will ask for no child support in return). Please let me know if this is something you would consider as we both want what is best for the kids schooling.
You