Joint custody question

Do you have to go through the courts to establish a binding parenting plan? Can you get a signed copy notarized by both parties and does that hold up legally?

If it does, and a child support agreement was made in the plan, does that meet child support criteria if payments were dated and documented? Like the ex couldn’t come after them for back pay through the court system later on?

Edit: I should add, this would be a temporary solution as no agreement is currently in place and there is a lot of planning and research needed to get the courts involved. Could this work for a period of maybe a year before going to court? The child is 9 years old