My question involves child support in the State of: new jersey

I pay weekly out of my check for my daughter 16 who lives with her mom. My daughters mother and I were never married. We have joint custody but she has physical custody. Three weeks ago her mom moved to another state and had my daughter moved into a converted garage with her 25 year old cousin so she can finish high school in that town. The garage is on the property the cousins parents. They tried to keep this secret from me but they were found out. Now this is a two part question. One, can my daughter even live without one of us and is so why does the mother feel I still have to pay her the child support. She is paying the cousin "x" amount and I said that is fine but i want the rest back, you are not raising her anymore. Then she went on to say that I should pay the cousin the full amount. I would think that we would have to share her expenses equally. I do not want to go to the probation or courts yet because I don't really want her to have to leave her school. I am not even sure if it legal for her to be living there with her cousin. I am 40 minutes away from her but it would be possible to have her live with me and take her to school and pick her up but that also is against the law. Thanks Keith.