You need a lawyer with Higher Education experience, as well as civil rights experience if your unconventional family structure is resulting in your being discriminated against. In Higher Education, and especially at the UW, there are many seemingly complex rules and procedures for students with grievances to follow. In some cases, the grievance process can be inadequate or lead to an inadequate result. I have found that when dealing with a large university, like the UW, familiarity with the university's hierarchy of bureaucracy is sometimes equally important as knowing the law. You have to know how to get to an actual decision-maker. A lawyer with this knowledge can (after conducting an investigation of the specific facts of your case) initiate dialogue with the University to assert your rights to them directly. There should be at least a few lawyers on this site with these specific qualifications that also offer free consultation, myself included.
Legally speaking, "Residency" can have different standards depending its purpose. If you are trying to establish residency for purposes of in-state tuition, standards can be very different from ones used for Medicaid or GED. The best thing is to find out what is causing you to be classified as out-of-state and find out what you can do to qualify for in-state tuition. Here is a link the rules that I am sure you are already familiar with http://www.washington.edu/students/reg/residency/domicile.html
Some Universities have promulgated a residency policy that goes something like this: "If you moved from State X to (for example) Washington FOR PURPOSES OF ATTENDING SCHOOL (any) you can not ever establish residency." There is a lot of good constitutional law floating around that calls the validity of such a formulation into question.
The other lawyers have given such outstanding answers that I can add little but this last is important. In addition to Civil Rights/Human Rights experience and in addition to Education Law, you need someone with expertise in Administrative Law. You are going to have some administrative remedies within the school. You must exhaust these remedies before you go to court. My hope is that you can actually WIN one of these stages. As noted by counsel, your situation is not a subterfuge to get in state tuition.
I'll be rooting for you. Most State U's would be proud to have someone with such a great story and focus as a resident of their State.