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If the boys came to live with the father, his child support would be eliminated for those children. He would still have to pay support for the girl, and this would be set off against the support obligation of the mother. So depending on his and her incomes, he may still have to pay support, or she might have to pay him support.
As for the withholding of visitation, she is not allowed to do that. It is her responsibility as a parent to make sure she gets there, it is not optional. His remedy in this case would be to file a motion for contempt, stating that the mother is willfully disobeying the order of the court by not allowing visitation as agreed.