It seems you'll be using the propane for heating and cooking for about a week. It will depend on the outside temps and how much you run the furnace. A small Class C will get warm very fast. We like to sleep without heat and just turn heat on in the morning when we get up. Even with our 40' motorhome it warms up in minutes. This would be one area of conservation you might consider. Bring your warm comforter along. Furnaces take a lot of propane. If you don't encounter cold weather your propane would probably last for your week. Also, you have the option of the hot water heater and refrigerator running on propane or electric. If you have electric hookups be sure to set them on electric.
Buying an electric heater just for your week of RVing in a rental doesn't make too much sense. However, if you have a small one at home or can borrow from somewhere, by all means bring it along. Keep in mind that they draw current and if you use it at Dead Horse the current was low as I recall so just be aware. Most campgrounds have 30A power and for that you'd be just fine.
RV propane can be filled at fuel stations where they have a large tank usually in the corner of the lot. You drive up, go inside if necessary to let them know you're there and they'll fill it for you. A simple process. If you're driving by a regular private campground many times they'll also have this large propane tank and will fill it for you. A campground would be more costly than a gas station.
If you leave for siteseeing for the day, most folks will just leave a chair at the site. However, if the campground has a post at the edge of the driveway to your site, usually you'll have a tag that you'll place on that post designating that you paid for that site. Campers are good at not moving into your site if they can see some sign of occupancy or a dated tag on the post. By the way, those posts have a way of a bad encounter with RVs. Be on the lookout for them.
If you're just connected to electric it will be a two-minute process to unplug, store the cord and take off. Even using all connections - water, electric and sewer, it's not a big time-consuming job.
I'll bet your wife won't want to stay in a motel when you get to Escalante. She'll love her own bed and playing house! :) Have a good trip!!