Legal Question in Landlord & Tenant Law in Washington

Yes. The landlord has nothing to do with your dispute with your spouse. That said, you can ask the court to order that whomever remains in the unit pay the rent so that the one who leaves can rent a new place of their own. It's not quite as simple as that, because a few other things will factor into the decision of the court, such as incomes of the parties to start with.