If the father stops paying his share, sole custody immediately reverts to the mother. These two dynamics will tend to motivate an agreement between the parents so they can get their child back, get rid of the monitor, and quit paying money. If the charge is fabricated, the mother is placed in the position of weighing how badly she wants revenge versus the continuing financial expense and her desire to be with her child and free of the monitor. If the mother stops paying her share, sole custody immediately reverts to the father. The overriding incentives are for both parents to compromise and back down from unreasonable positions.
Child abuse is an unreasonable position as is making fraudulent charges of abuse.
The parent's knowledge of the inflexibility of the system will also work as a deterrent to future problems. The same logic can possibly be modified for use in claims of physical abuse, sexual abuse, drug abuse by one parent, alcohol abuse, harrasment, and even abuse of custody rights. If one party is indigent or not working, there is a problem of extracting payment. A solution might be assigning the nonworking spouse to part time duty with the California Conservation Corps to work off the payment. Abused children can be protected even if the abuser lies to the court.