First, you don’t absolutely have to have the house spotless to sell it. You’ll get a lower price – but will the difference in cost be as great as the cost of an RV?
I have a daughter with a lot of anxiety issues and OCD, so I know how hard it is! Part of the way through is finding a *new* routine, so it’s not a pile of unpredictability.
How about a plan like this: you need three things: a motel that can accommodate your family, a motel or kennel for the pets, and a strong helper, and possibly an assistant for the kids. Book six weeks of Saturday nights in the same room at the motel, including one for practice, and book your helpers. Saturday afternoon take the family over the minute it is check-in time. Then you and strong helper go back and clean up the house. It won’t be perfect, it won’t be taged, but you can get it half-decent. With a regular weekend routine, it’s predictable for the kids and less stressful for you. And at the same time you can do the decluttering and box up what you can (although I’m guessing with 9 people in 1500 square feet you already don’t have too much excess, you don’t have room for it!)
Do the math – how much does six nights of hotel rooms plus two helpers plus , say, a 5% loss of value on the house cost, compared to the cost of an RV? (and the time and maintenance you would have to put into an RV, and the kids running in and out of the house from the RV because you can’t keep them locked up…)