Of course, he/she can baptize as long as the mother is not against the baptism. In practice, we can baptize, but the condition is that the parents should consent to the baptism.
If it is against the will of parents, the church does not allow baptizing children against the expressed will of the parents. Only in the case of danger of death, of life, here, yes, we can baptize a child, an infant, or a child, against the will of the parents. In this case only.