A question about the legal consequences of "baptisms"?

Tweet

Assumed case: A married couple, one is an atheist, the other Catholic (or Protestant or whatever) The "faithful" parent manages to get hold of a priest who baptized the child at the request of that, there is an entry in the baptismal register, and the child is now a "Church"? Without the knowledge of the other parent part? Is this legit or even possible? Are committed to a "christening" both parents or guardians to sign? My son suddenly wants to leave our grandchildren to make "Catholic," my daughter wants this in any way. Contrary to all agreements BEFORE the marriage will be his children suddenly BUT to "Christians" made??.