I have a better idea.
The duped father should be able to choose between demanding full custody of the child (the mother is obviously unfit), or, if the mother refuses this, terminating all financial support and continuing visitation; he can apply his money directly to the needs of the child while visiting him.
That’s an idea. The only problem is that you make a pretty big presupposition in saying the mother is by definition unfit in this dynamic.
If you can say ‘when the mother is unfit,’ it would be better. But the fact that a woman has an affair and cheats on her husband doesn’t necessarily make her an unfit mother to her child.