Yes a father can take a child away from his or her mother but only through a court order.
The father would have to take the mother to court to legally gain custody of the child.
Still the father can take the child with them away from their mother as long as they are not divorced yet without a court order.
It would not be considered kidnapping since the father has custody of the child along with the mother.
But if the mother is deemed unfit to be a mother and the father wants to get custody of the child and take him or her away from the mother then they will need to go to court and have the court grant custody of the child to the father from the mother.
The father cannot just show up at your house and take the child away without a court order for custody.