Some things to consider.
Three dogs, two adults, and a child in a motor home might be a bit crowded. In a smallish Class C, you are REALLY going to be crowded. Dogs are 'relatively active' and could make things interesting.
When you get home from flying after 7 days, do you really want to immediately hit the road for another 7, driving, stopping, driving again, flying, driving stopping driving... do you really think you could sustain that over a lengthy period of time?
800 mile drive is a two day affair, unless you really bust your butt on the road. Lets assume you do the 800 (worse case) in a day heading out to wherever. Given that you are a pilot, I assume you have a crew rest requirement the day prior to your next flight. So, you certainly wouldn't be able to do 800 on the return leg... So, lets say 1 day out, 2 days back, and probably a preference for a day of rest before you fly. So, you're down to 3-4 days.. maybe more if you stick closer. But, I think you get the point.
I'll give you the same recommendation some of us in the forum recommended to someone else looking to straight from a brick and mortar house to full time. Rent an RV and give it a shot for a few 'rounds' of your schedule. See if you think it's doeable before you sell the house and buy the rv.
Just thoughts...
Mike