You seem to have several concerns. All of these issues can be dealt with after a consultation with a local family law attorney.
Dear New York spouse:
You really need an attorney. Taking the children and moving out of state without your husband's consent is kidnapping.
I cannot stress how important it is that you hire a family law or matrimonial attorney. Even without your name on the deed you may have a marital right to the home. A court may award you custody of the children, as well as child support and spousal support. If you do anything on your own, you risk the loss of the children, your freedom and financial support.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
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