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It is unlikely that the girlfriend can succeed in collecting support. Her husband is the legal parent of the child and will remain so. Court's have a very difficult time illegitimizing children. Even if you husband becomes the "legal parent" he will not have to pay back support for 12 years. The mother's husband was the legal parent, and only one father at a time is responsible for support. The best the mother can do is request support from the time of the petititon to establish paternity and support for the child. It would certainly be no earlier than the time of her husband's death.
My own opinion is that unless you push for paternity, a court will find for the mother in her attempt at collecting child support from your husband.
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Please be aware that my answer is not legal advice, it is merely information and no attorney client relationship has been formed. You should always contact a local attorney for legal advice.