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If the father has decided to give up any visitation/custodial rights under the custody agreement, then if this is a permanent decision, the mother could file a petition with the court to modify the custody agreement and ask for child support to be increased to reflect that she is now the sole custodial parent.
The custodial order grants the father the right to have joint custody, but these are rights, not obligations and he can't be forced to exercise his rights to custody. But if he chooses not to exercise them, then he would be obligated to pay more in child support (if he is paying anything now) so as to ensure that the mother has adequate support to care for the child.