"who has the final say in it?" The court has the "final say in it". However, unless the agreement by the parents is obviously not in the child's best interest, the court generally would not object to a parenting plan agreed by the parents.
For example, if the parenting plan requires the child to be alternating household every other day, the court likely would not sign. Another example, if the parents live in different states, the court likely is not going to accept a parenting plan that requires the child to change household every six months.
In WA, the courts also have to check the backgrounds of all adults living in each parent's household before signing the final parenting plan. If, for example, one parent is living with a convicted child sex offender, the court likely is not going to sign any parenting plan that provides for the child to spent time with the parent in the parent's household
You should review the local rules for the court hearing your case. The local rules will have the procedures that the parties must follow to present the final orders to the court.
Until the child is a legal adult, a parenting plan is not "finalized" in the sense that either parent may ask the court to re-examine the parenting plan when a statutory basis exists.
You should review the specific facts with your attorney to find out your legal options.
You haven't indicated whether this is in conjunction with a pending legal proceeding, such as a modification. If there is a proceeding, the papers are presented to the Ex Parte Commissioner of the Court. If the matter is in Tacoma, that's in Room 105 of the court house.
This post is not meant to be legal advice for a specific situation. Additionally, it does not constitute an attorney client relationship. It is always recommended that you consult with the attorney of your choice before taking action which can affect your legal rights.