Welcome to the RTA Forum!
What do you hope to gain by using an RV for this trip?
RV's can be great if you want to take a vacation and explore the country, especially if you want to explore the national parks and other scenic spots.
They aren't great for making a speed run across the country. 600 miles with 2 people in a car each day isn't a big deal, but that's a lot of miles to cover in an RV, especially on multiple days in a row. They are slower, use a lot more fuel, and it takes time to get set up and to get back on the road, especially when you are still learning how to operate the RV. Most people I know with RVs tend to limit themselves to 400-500 miles in a day, and that's on travel days.
Also, if you're renting your RV on Sunday, you probably can't pick it up first thing in the morning - and whenever you do pick it up, there's time needed for orientation to show you how to actually operate it. You'd probably at best end up with just a half day on Sunday, compressing your timeline even more.
With that kind of schedule, I just don't see where you'd get any advantage out of the RV.
Have you considered just using a regular car for this trip - either renting or using your own? I think that would not only be cheaper, but also more enjoyable and give you more time to actually stop and do a little exploring.