You should be fine as long as the marriage was bona fide at the time of marriage. Hopefully you can work on your relationship and maintain the marriage. You should consult an attorney for a more comprehensive evaluation of your case.
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Yes, provided you married is bona fide, as to the parentage of the child, if one lives in a marital relationship the presumption the child is of both parents unless proven otherwise by the DNA test, which does not seem to be the case here.
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I would only add that I think that you need to be completely honest at the time of the interview. Many USCIS offices will be hard on any applicant that they feel is not being completely honest. Meaning if there's even a question as to whether or not the an answer you give is the truth, immigration will not give you the benefit of the doubt. My guess is that you and your wife will get questions regarding the child and should be prepared to answer them. You should consider hiring an attorney to prep you and go with you to the interview.