Shuttle service from campgrounds in Moab?

No shuttle service. One can hire a guide service who will tote you around the parks, but that won't be cheap. Both parks have multiple parking areas from which to do short strolls to longer hikes. As noted, rent a car or a jeep if you need to get around for the day. Probably easier than finding a parking spot for a large RV, esp. in Arches. If you rent a jeep, after touring Island in the Sky at Canyonlands, you can drop down Shafer Trail and head back to Moab along the river.

PM me if you have other questions. We spend quite a bit of time in the Moab area every year. I camped there a total of five weeks last year.