All Over the Board, Indeed
Welcome aboard the RoadTrip America Forums!
With little more than a destination and a time frame, it really is tough to offer much specific advice. I would say one of the larger determinants in figuring out where to start and what you can do would be to figure out where you can get a one-way RV rental at a reasonable cost. Notice I said 'reasonable' and not inexpensive. One way rentals on any RV large enough to keep four adults from each others' throats over a week and a half are going to be considerable. And don't be fooled by the base rental price. You also have to pay extra for 'equipment' - kitchen supplies, bedding, eating utensils, etc. Then there's typically a mileage charge as well (unlike the unlimited mileage you might be used to on car rentals), and the cost of a spot to park it each night. So that's really your first order of business. Start checking out some of the larger rental companies such as Cruise America, El Monte RV, Apollo RV and others to see what one-way RV rental deals they may have on offer in the western US. I would suggest that you go to their websites, get a phone number, and talk to a real human agent who can help guide you to the best deal that they may have to fit your needs.
But even before you do that, I would strongly urge you to cut back on your expectations. RVs are ungainly on the road, and despite what you may think take a fair bit of time to get parked, set-up and ready for a night's 'camping', and then more time the next morning to get everything stowed away for travel, get from you secluded campground to the nearest actual highway and back making ground towards Seattle. I would be very surprised if you could, say, fly to Phoenix, rent an RV, get familiar with it, and then get to Seattle via the Grand Canyon, a red rock park or two in Utah, some of the Cascades and finally some of the northern Pacific coast all in ten days, especially if those ten days include your two flying days. Bear in mind as well that the 'estimated drive times' that you will get from computer-based mapping programs are a total fantasy even when you're driving the family sedan at a steady 75 mph on the Interstates. In an RV on the two-lane roads of the magnificent inter-mountain west, I'd double the times they give you. I'd probably try for a 'start' to this trip in either Salt Lake City or San Francisco, so as to leave yourselves time to actually get out and enjoy the places you can get to between those cities and Seattle.
But again, your first order of business is to start contacting RV rental companies and see what kind of a deal you can get on a one way rental, and whether that fits into your plans and budget.
AZBuck
There is an advantage in using an RV Outfitter
Given the constraints of your trip -- I would suggest you look at using a RV outfitter. The huge advantage is that they can take care of most of the logistical details of your trip -- pre-checking the RV, outfitting it, booking campsites, arranging for supplies and your only tasks are then limited to driving from point A to point B and so forth.
Plus, since they do this every day of the year, they have a firm grasp on how long it takes to drive an RV from one place to another and their routing suggestions can make a huge difference when someone, like yourselves, is trying to fit a large trip into a small time window.
Without doubt, the best RV outfitter in the business is Tracks and Trails Even if you elect not to use them, I recommend checking out their website. It is chock-full of ideas and gorgeous photography. The site has lots of useful information, but to save you time, here is how they do their pricing. One thing you'll realize is that their company is based on similar philosophies that you will find here and a part of that is that you will need to give them as much information about what kind of vacation RV trip you want to do. They can plan just about any scale trip you can dream of -- what they can't do is bend the rules of space and time. Like Midwest Michael mentioned above -- driving an RV takes more time than you might expect and there are no "Real" shortcuts. I lived and worked in a RV for 6.5 years continuously so I have an appreciation for the pluses and minuses of what you are envisioning. Some of our moderators have driven thousands of miles in RV's as part of their road trips -- it can be a fantastic way to travel -- but you have to allow 3+ "extra hours" every day for set-up/striking from camp sites.
Mark