in WA state does a 13 year old child have the right to decide which parent they want to live with

No. Absent an agreement of the parents, the only person who can make a decision regarding custodial arrangements is the Judge in your particular case. Once the child reaches the Age of Discretion, which is different for every kid, he/she may express their wishes to a court through a third party (Guardian ad litem, Therapist, etc) and the Judge may or may no take those wishes into consideration when making a decision regarding custodial arrangements.