I didn't have an RV, and I didn't go as far, but going from NJ to CO in my Tahoe with a car full of "stuff" towing a uhaul and a Newf who had way more room than his humans, the trip was a breeze. I'd never send him in a plane either, and have pretty much traveled the country with the dogs by now. Was easy, peasy in the Tahoe, so I can imagine would be even easier for you. Best advice I can give you is pre plan your route for when you will stop along the way. Have designated places that you plan on staying. Know hotel chains in the areas just in case you don't want to spend another night in the RV. Know how late you are able to arrive and if you need an advanced reservation if you plan on going to camping sites and their rules on dogs. And I always look up emergency vets along my route just in case I might need them (also because I'm a total freak about my dogs
Bring lots of bottled water, familiar toys/blankets/beds (don't wash them just before you leave so it still has the smell of home on them). Enough food and know where to stop if you will be needing more so you know who sells your brand (or just bring enough until you can find a place who sells in in Seattle). Bring along a doggy emergency kit filled with benadryl, etc. and copies of your dogs vaccinations. Also, you may need a ramp or folding stairs to get in and out of the RV for the dogs. And I always bring at least one extra collar and one extra leash just in case. And a stack of towels in case you go for a walk and find some mud, puddles, rain etc. It took my in laws 3 days to get here from FL and they weren't pushing it- just to give you an idea on timing
I'm the kind of person who refuses to stop, so if you have a pre planned place and reservation in advance, it kind of forces you to. (PS best hotel chain by far for the dogs was Holiday Inn Express- awesome experiences across the country). One last thing, make sure you make a quick stop at your vet before you leave and ask for your dogs health records. Keep a copy for yourself, and one for your new vet when you get to Seattle.