Use KOA, buy the membership to get tje 10% discount. Then you have consistant amenities all the way. Take interstate 15 through to Las Vegasthen west from there.
If you guys have not planned your route yet, consider driving south into Montana. The end on the first days drive at Glacier National Park (east side). Nice place to enjoy your morning coffee. And since the speed limit is 80 MPH you should make it down to Idaho in no time. Unless, making your way through Yellowstone National Park interests you. The Grand Tetons Drive. of Yellowstone by Jackson (Wyoming). has a majestic grandeur that is worth the drive alone. Utah has something like 7 National Parks, only one or two I've been too. Stop in Las Vegas and stay at a fancy hotel with a pool for the kids. I think hotel specials are available on Groupon or google search. As a kid it's unforgettable. (Waterslide that goes through the middle of a shark tank.). Have fun, the Great American Outdoors is the way to go. : )