AZ 160 , AZ/UT 163 and UT 191 Insights

Your planned route is an easy drive with your MH and trailer. We've done it often with our 40' towing the Jeep.

All good 2 lane roads. Valley of the Gods is a good car tour.

Adding to the above list would be Bluff Fort. You might also consider staying in Monticello and taking a day trip out to the Needles District of Canyonlands.

I believe the steep grade and sharp turn are near Bluff not Mexican Hat. There are several interesting places to see along this route between Monument Valley and Moab including:
UT-261 the Moki Dugway
Goosenecks State Park
Hovenweep National Monument
Natural Bridges National Monument
Bluff Fort
South Fork of Mule Canyon and House on Fire
The Valley of The Gods
Sand Island Petroglyphs
Edge of the Cedars State Park
Dinosaur Museum
Needles District
Newspaper Rock

The road is two lane, but not a problem. There's a good sized grocery store in the middle of the reservation..at Kayenta, I think, that makes an interesting stop for last minute supplies. At Mexican Hat, your entry will be down a very steep, short hill that has a dog leg turn to the right at the bottom..just take it slow and you'll be fine. If you like to take off road drives that are a bit hairy, stay over in Mexican Hat and take your toad to drive the Mogi Dugway road to the top and back, an easy day drive with great scenery.
South of Moab, there is a tourist stop called Hole in the Wall.. it's interesting, but just up from it is a nice rest stop if you are so minded at the time.