It is only about 12 miles from the north rim to the south rim. The hike will be somewhat longer, due to switchbacks, etc. But the drive is 213 miles and takes about 4 hours.
I have never driven from one rim to the other, but I have been on all of these roads at one time or another. There are no mountains in the area but there is a bridge over Marble Canyon. This is the only place you might have a problem with heights.
The North Rim is heavily forested, reminds me of driving through Yosemite or Yellowstone. As you drive east it becomes drier and more barren. You pass the Vermilion Cliffs and part of the Painted Desert. It is isolated and you need to plan your stops. Some people don't like this type of scenery, but I find it beautiful.
I have never been to Rustler's Rooste. We used to live closer to that part of town and went to a nearby restaurant called Top of the Rock. We only went there for anniversary or birthday dinners.
I did see your post last evening but thought I would wait until morning when I could focus on a proper reply.
nacl