Is it right for a man to pay child support to a mother who didn't keep his children?

No, child support is suppose to go to the care taker of the child. That's why it's called child support. Your paying the care taker the cost it takes to raise and care for the child. If you pay the mother who didn't keep the children your giving her the money. That would be a sucker move.

If the mother didn't keep the child I would go to court and change the child support to the person's name who is caring for the child. The courts have the power to do that.

if he owes her back support then he will owe that to her until he dies. in this case it only matters that she had the children at the time that he owed her the money but didn't pay it. it doesn't matter if the kids no longer live with her or that they are now adults.

if this is current child support then he owes it to whomever has the children & he needs to go to court to point out that she no longer has the children & that the money he is paying for the children needs to go to whomever now has the children.

so, to recap: money that he owes her from the past when she actually had the children is money he will owe her until he dies or pays it back. it's not going away regardless of where the children are.

money that is for the children's current care should be going to the person who has the children now, not her & he'll need to go to court to get this changed.

No! It's called child support to actually support the expenses the other person is paying for the child. Not to support a child you don't have or are paying for at all. You can definitely dispute this in court.

He should still pay child support, but he should be paying it to the person / people who are actually raising his children for him.