I am leaving my boyfriend of 5 years and we have two small children and he went to family court and got an order stating he wants sole custody and that I cannot move out of state.
What can I do about this New York is to expensive for me to live what are my options

If he gets sole custody, you can move anywhere.

Where in NY do you live, NYC?

If you can't leave the state, you can move to another part of it, a cheaper part. Example, Western New York. (that is, I think western NY is a cheap place to live, could be wrong though)