In that situation the father would have to petition the court for paternity, which the mother would contest. The father would have to request a DNA blood test on claims that the child is his, and that he wants proof of biological paternity. The mother can attempt to contest it, but if the father provides evidence that the mother permits the other parent to put the child off as his own, shares custody, and splits expenses, the judge would allow the test to go forward, most likely.
Then, when the result would come back and it would be positive, the father would then formally file a petition to assert his parental rights
and add his name to the birth certificate. With evidence, and with the child's age it should be granted, even if the mother contests--usually the courts become less likely to grant requests once the children are older than 2 years old. Then, once parentage
is assured, the new biological and legal parent can file for formal custody and visitation, but more importantly for the purposes of your book, can refuse to grant consent on the adoption. That will block the other mother from adopting the child out unless she either gets the father to agree, or she gets a court order permitting adoption to take place, which would not happen if the other parent is active in the child's life.
Edited by Dimitry Alexander Kaplun on 11/1/2010 at 6:02 PM EST