Hello and welcome to RTA !

An RV can be a fun way to travel as a family if it is your 'thing', but it will not be the budget friendly option compared to a car and family Motel room. Not only is the rental expensive from the start, once you have added mileage charges, kitchen and bathroom kits, high fuel consumption [8-10mpg] and campground fees, it starts to add up. So if it's a Lifestyle choice and your budget can manage it, it's a great way to see the National parks.

It's a very popular trip and you will find a lot of info by searching around the RTA site. A loop works well, heading south down the coast from SF to LA [possibly San Diego and back to LV.

back to vegas?? but would rather not!]
Then don't ! lol If you want to see Death valley then just drive through but DV will be extremely hot in August so a 'drive thru' might be best. If not, from Zion you could take a more direct route to Yosemite via Tonopah and the ET Highway. You would need to book lodgings/campgrounds in the NP's well in advance when travelling in August.