The system may be wrong, but a child is still a child… and here we have 2 grown adults punishing the child for wanting to live at their other home.
Young children can't decide where they want to live, so we're really only talking about the last few years of cs. One parent already benefitted the majority of the child's life by having extra time with the child and having extra money. By the child switching homes it the teen years, I would assume it had more to do with their relationship with the custodial parent rather than simply the other parent bribing them.
There are laws that stop young kids from being manipulated into switching home, but by their teenage years they are more than capable in making a decision on where they want to live. Sometimes teenagers might go back and forth a few times between the homes. They should never be put in the middle of financials and especially bickering parents.
Why is the daughter looking to impoverish the mother as opposed to just wanting to get away and live with her dad? If you believe that cs is just for the parent's pocket and not the child, then why do you think the child is thinking about money in making this decision.
CS needs to follow the child to cover the extra costs in living, food, activities, etc (moreso in this case where it would be over 60% of the time - actually 100% because the mom won't allow the daughter back if she leaves).
While it seems like you’re coming down on the child, is your position that the child is free to live in whatever home but the cs payment should stay with the same parent forever?