I'm about to move from Calif. to Washington State. At what point am I required to re-register my car?

I'm about to move from Southern California to southern Washington State. My car is an older car that wouldn't be worth much (a 1988 Toyota Corolla), but it's in good repair. It's registered jointly to my parents. My parents are currently in the midst of a divorce. My dad is trying to officially get sole ownership of the car, and has said he will be officially transferring the title into my name once he has. My mother has been making a point of trying to stalemate him on more or less everything he's trying for in the divorce, though, because she's very angry with him and wants to waste as much of his money as possible. As such, she's likely to be uncooperative when it comes to helping re-register the car in Washington. I'm using the car with my parents' full consent. At what point could it become a legal problem if I'm using it in Washington but it hasn't been registered in Washington yet?