I don't think there is anything you can rent for the amount of money you might save on gas. Anything full profile is going to take as much or more gas to move it, as your truck and TT, so a C might be $1500-2000 a week and use even more gas (but sure nice for family travel). You might find a small popup for $500 a week, but added gas cost, over just the truck, will be about half the added cost of towing your TT.
Allow 4 days going out to GC-Moab-SW Utah parks, about the same going back, leaving about six days for visiting and traveling between parks and other sights. I tend to look for places enroute, so each travel day is at least a couple hours visiting something interesting. What happens to be interesting is very much an individual thing, I like historical sites and geology, othersmay want outdoor sporting activities or nature activities like hiking, and still others shopping malls and theme or amusement parks (thus no way I could take my sister's twins on a trip I would like).
My childhood experience was that the only really bad road trips were those that were too ambitious, i.e. the whole vacation time spent in the car moving place to place on the "must see" list. E.G. Grand Canyon and/or Las Vegas, LA and Disneyland via Las Vegas, Black Hills and Yellowstone, or Colorado Rockies and Canyonlands might eac work for two weeks from the Great Lakes (Detroit for us) but Yellowstone and Grand Canyon in same two week trip is a problem because for two weeks we would never stop driving long enough to see something.
FWIW my last two SW trips, slightly longer than 2 weeks each, from central Oklahoma:
Guthrie - Great Salt Plains Lake - Dodge City - Bent's Fort - Pueblo - Royal Gorge - Curecanti NRA, Black Canyon of the Gunnison, Colorado NM - Green River - Moab: Arches and Canyonlands - Monument Valley - NW New Mexico - Palo Duro Canyon - Home.
Guthrie - Route 66 museums in Oklahoma - Bosque Redondo - Roswell - Lincoln County - Ruidoso - Alamogordo - White Sands - El Paso - Davis Mountains - Texas Meteor Crater - Red Rock Canyon - Home
Just a couple of two week circle tours, lots of places in Colorado, Utah, Arizona, New Mexico, West Texas bypassed because we'd been there already or they need more time of their own. Also, that's my SW, because to me Nevada beyond Las Vegas down at the tip, and any part of California, are part of my Far West, beyond a reasonable two weeks from where I am close to the center of the lower 48.
I did these at a pace such that no day was exclusively a travel day. Any route you take across the U.S., any day you move more than 250 miles, there is at least one place that is interesting to somebody to stop and see for at least an hour or two. At the same time, we stayed no longer than two nights in any one place, even some places where other people go to spend the whole two weeks (or several months). Finally, some places where I had planned 250 or 300 miles of travel in a single day, I found reasons to take 3 days instead.
Tom Test
Itasca Spirit 29B