I’m from California and I’m about to begin my senior of high school. University of Washington is my first choice but of course, it’s extremely expensive for out-of-state students. If I do happen to get in and if my parents move with me to Washington, could I get in-state tuition for my sophomore, junior, and senior year? I’m assuming I would still be living in the dorms and not at home.
It looks like maybe. Go here for info:
https://registrar.washington.edu/students/residency/residency-requirements/
The question I’d have you ask U Washington is if you can qualify for residency after you’ve already been an out of state student for your first year. That’s the trick.
Generally you would have to live in Washington state for a full year without attending any college there. If your presence in the state is to attend college, that doesn’t count. Otherwise all out of state students would get in state tuition starting sophomore year.
From the link that @RoaringMice posted, it looks that your plan is unlikely going to get instate rates.
Why is UWash your first choice.
My cousin let her DD start there with the wild-haired idea that she could get instate rates on her own some way. After a year of unaffordable instate rates, her DD quickly married her Wash-resident-BF, and then later qualified…but I wouldn’t recommend that.
^ 
There’s got to be a better way to come up with the $24K (or ~ $18.5K if receiving OOS scholarship) difference!
Are your parents actually planning to move to Washington or is this wishful thinking? Your parents should want to move there for other reasons, because it’s doubtful this would work to reduce your tuition, and then they will have uprooted themselves for no good reason.