The father who abducted his children did not have the right to take them from their home. The mother was in charge of the children and they were where they belonged. Anyone who takes them away with out the proper care takers knowledge is in the wrong even if it the dad.
It is an awful thing when children have to witness the domestic violence in their own home. And if there are custody issues, the children should not be aware of them and should not be used as hostages. So that father was wrong to take his own children in a forceful way.
No, he did not have right to take the child from the other parent's home without her knowing. If both of them are the parents of the children that there should not have to be any sneaking. Even if she call the police, he has just as much rights to the children as the mother, but to come while she is not there and take the children is not right. She may not have known who took her children. That was a childish and very inconsiderate move on the fathers part.
In cases of child custody, a judge must make a ruling. One parent cannot simply abduct their children without the permission of the other. If there is a dispute, both parties have the right to hire lawyers in order to plead their cases. The law has provisions for such disputes.
No, a father who abducted his own children from their home does not have the right to take them without the mother's permission, because a mother is presumed to have custody of a child unless there is a court order. If a father wants custody, first he needs to prove paternity. With a court order, she can prevent him from taking the child.