Mineola Litigation Lawyer.
He has the right to file for joint custody. It really depends on the reasoning he is incarcerated. If he was charged with a violent offense against the mother of his child, or against the child, then the factors would weigh against him. The amount of time he is spending incarcerated may play a large role as well. He would need to hire a lawyer to go to court
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Instead of sueing him you cab bring a violation against him for not paying the support to you (assuming there is an agreement) and then in that same violation you can ask for all if those other costs because they are residual effects of him not paying you.
In the matter of a separation, your spouse will be kept on your insurance policy unless one of two things happen: (1) She agrees in the separation agreement that she will get her own insurance, in your case it would be from her job, or (2) or you get a divorce, where you both sign a DRL 236. The DRL 236 form is the notice to the parties that if their receiving health insurance from eachother it will terminate upon the judgement of divorce being signed. In New York State the DRL 236 is required.