Since this will likely involve changing the school district, you will need permission from dad OR the court to move. If dad agrees, then you have no problem. You will need to notify him and give him the opportunity to object.
If Dad doesn't agree, then you'll have to present an argument to the court as to why it's better for the child(ren).
Since you're willing to provide the transportation, Dad can't use that argument against you.
So why is it better for the kids? Be prepared to provide a well-thought out and documented argument.
It's been over 15 years since I lived in NJ, but IIRC, Middlesex county is safer than Mercer county and has better schools. If that is correct, gather evidence to support it and to help justify the move if Dad won't agree.
But hopefully you can work it out and just send it to court as a stipulation. Since you'll provide transportation and the kids will be in a safer neighborhood with better schools (if my memory is correct), I would hope that Dad would be OK with it.