Roundtrip PA to CA in the fall??

We're experienced travelers with dogs. Not so much with the birds, temperature control is an issue for them. We had a VW camping van in the 80s in a pop up camper for a few years before getting the Class C. We are limited to 5 weeks because that's how much vacation my husband has (he's not retired yet). We're visiting my 88 year old mother in CA and her wish was to see the entire "crew" and this is the timeframe we could do. We love traveling with our animals...it's pretty much a lifestyle at the point of having 4 dogs. We've always managed to find campgrounds. Have done 70 several times when just pushing it to get somewhere. Was hoping this would be a little more leisurely although not enough time to really sightsee.