Legal Question in Family Law in New York

The answer is that custody can always be changed. However, who are you related to the child? Since you reference child support, I assume that you are the other parent for the purposes of this response. There are details that would be helpful in giving you the most accurate answer possible that you have not included. For example, has an order of custody every been issued in favor of the custodial parent? If yes, then you as the non-custodial parent needs to show both (1) that there is a change in circumstances related to the care of the child, and (2) that change has made it in the best interests of the child to change custody to the non-custodial parent.

While the custodial parent not having their own home may be a change of circumstances, that in and of itself would not, in my opinion, be compelling enough to justify a change in custody. The fact that the custodial parent is moving often with the child over a six month period is clearly not good for the child, but the inquiry would not stop there.

Changing custody is quite complex, you really should talk to an attorney in person, and quite frankly you should hire an attorney for this kind of matter as you are facing a difficult battle.