Can we move out-of-state without permission from other parent?

Generally, under Washington statutes a 60 day Notice of Intent to Relocate must be filed and notice given to the natural mom to give her a chance to object to the relocation.  However, if the parenting plan is a Washington State parenting plan, and mother has no rights to visitation under the parenting plan, you may not have to give notice.  Please review your parenting plan with a Washington attorney to determine if notice is required in your specific case. 

No, you can't do this without permission, either from the mother or from the court.  It isn't in the parenting plan because it's a fairly basic provision in the law.  However, I don't think this would be hard to do, if you do have to go to court for permission.

This used to be harder to do, but courts now understand that a custodial parent's quality of life is important for the child's best interests.  Moving to be closer to family is a legitimate reason for the move, and if you can show that the schools in your planned new home are just as good as the ones available where you are, you should be good.  The parenting plan has to be adjusted, usually, to provide a way for the non-custodial parent to maintain their relationship with the child, often by longer vacation periods and sometimes by a reduction in child support or other means of splitting the increased transportation expense, but the court might allow that to wait until the mother is out of jail.