We did that trip last summer... the roads are no problem. We were in a 43' MH towing a pickup truck. You asked about RV parks... here's where we stayed. All FHU
Zion - Zion River Resort - paved interior roads,grass between sites, pool
Bryce - Ruby's Inn - very dusty, we were in the lower section - no shade or grass
Capital Reef - Thousand Lake RV. Shaded,grass between sites, pool, dirt interior roads
Moab/Arches,Canyonlands - Portal RV Resort in Moab. Paved interior roads, grass between sites, shade trees, pool if you are in the resort side of the park
We also went to Monument Valley and stayed at Gouldings` RV