You need to consult with local counsel as soon as possible. Some jurisdictions hold that if you're married to someone and they have a child, the case can be made that it's your child. Furthermore, you need to be very careful about your health insurance policy because it could be considered fraud if you allow her to claim benefits. You do not want that. Get a quality New York Attorney -this is not a situation where you want to represent yourself at all.
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Is your separation a legal separation? If so, you're OK. If not, get a divorce.
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The insurance is the least of your worries, as the presumption is that this child is yours and you could become obligated for its support. Consult an attorney now to protect yourself.
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