my daughter has 2 children from her ex boyfriend, they live in Rochester Ny. He pays child support but very little. Is she allowed to move out of

Child support generally doesn't control the amount of time a parent can have custody.  She should check with a lawyer in her jurisdiction.  He can probably contest any move she would make and she may need to provide him with notice of her intention.  She may need to prove to the court that it is in her children's best interest to move and have a plan in place as to how she would keep the relationship between them and their father.