The move away criteria vary a lot by state--so look up and tune into whats important for NY and focus your point on same==probably why its beneficial for child to move.
I agree its probably helpful to log Dads current visitation usage carefully and use that level and not his max possible to make point that dda not being major league shorted.
Do you have jobes in NC
Be careful about making pay for travel committments you may not be able to keep --I read here of Moms who manage to move away and agree to pay but a fraction of trsnaportation costs.
A teen with an active social life my try to kill every other weekend away--so be careful.
I suspect ther are parts of NC that do worse as to education than parts of NY so get your facts in line and clean.
Moving away to possibly get married to boyfirend sounds a lot different than moving with new husband to take new job he has been offered that will get us a better lifestyle ??