If both parents agree to change custody arrangements for the best interests of the child but don't want to stop or change child support is that possible?

Child is having problems at home
Mother and father think they want to try changing the child's home to the fathers.
Mother and father don't want to change child support.

I guess my question is. Do we have to change/modify child support if the living arrangements change? Can we just keep the order of child support the way it is?

Custody and child support are separate things.Child support may be increased or lowered without changing the custody.Custody may be changed with/or without changing child support payments.

I would strongly advise formalizing any change with the courts. If both parents are agreeing to the change, then the court will generally just rubber stamp it. But if you go against the court order without formalizing the modification, you could be opening a can of worms later.

But the answer to your question is that, yes, you can change the child's primary residence without informing the court.

If the child goes to the fathers home from the mothers, as long as the father keeps paying child support to the mother then they don't have to change it. But the Father is obligated to keep paying the mother even if child is living with him, unless they change the court documents.

If he does not, mother can at any time come after him for back support

Thanks for your information!