Indeed, your plan will not work in Washington. Places you want to see are just too far apart. The mileage may look doable, but travel times can be very long, especially on the Olympic peninsula.Much of the time you will be driving at 35-45.
My advice is like the guy above: just head on out to the Olympic peninsula via North Cascades and ferry. There's plenty there for a couple of days.
Skip Seattle -- too busy, not RV friendly.
Stop near Mt Rainier (La Wis Wis is good) on the way back.
Then carry on toward Idaho via US 12.
