You may be able to file a Non-Parental Custody Petition to establish custody and request child support from either/both parent(s), depending upon the circumstances. Starting in 2021, Non-Parental Custody Petitions will be replaced by Petitions for Legal Guardianship. (RCW 11.130.190) A parent may consent, or have had parental rights terminated. Or, the court may find clear and convincing evidence that no parent is able to exercise the powers that would be granted to the guardian of the minor.
If you are a relative who has had a substantial relationship with the child(ren), you may be able to petition the court for visitation with a child. (RCW 26.11.020) There are a list of factors the court considers in considering the request.