You're in my favorite part of the country - I'm from there, or therabouts. Whereabouts in Eastern WA are you? If you're prepping for Mt Rainier or Mt St Helens to blow, remember that ash from Mt Mazama was 3 feet thick in Idaho after it blew. Of course that took months to accumulate, something else you want to be prepared for. I had friends in Portland when St Helens blew in 1980, to my knowledge they had no special survival preps but they made it through OK.
That said, I'd take the RV first. If you can manage it, the Tahoe would be a nice get-around car once you reach wherever you're going (it will be hard to take the RV on a run to the Circle K to get milk), but in the case you can't take both definitely opt for what will give you and your family the best chance, e.g. the RV. A little hard for four people to eat, sleep, cook, and poo in a Tahoe for a week or two. The RV shouldn't have that problem. Don't worry so much about being a target - arm yourself and sleep light, but it isn't going to be Mad Max time. In my mind, it isn't even a question. Head East or Southeast (Mazama ash reached Missoula, but not Reno), hunker down and play some cards. Then go back home and bust out the shovel to find your home again.
Do not give in to evil, but proceed ever more boldly against it.