I guess you already went on your trip, hope you had a great time.
For others that are going in the future-
I'd recommend skipping the switchbacks- the road from Potash is worth the drive. We love it. You will see very few people and it's a wonderful drive. I prefer it to a lot of other roads in the area. The switchbacks are fun the first time, though.
As far as the rest of the gear you suggested- keep in mind we take more of a minimalist approach-- the trail is ~100 miles- just fill up before you go- maybe a 5 gal can if you feel so inclined. You'd have to get 5 mpg to begin to run out of gas. Tow strap- always, but winches are not needed, neither are compressors, or tons of extra parts. There is sand, so you may be more comfortable with hi-lift jacks and the like. I quit bringing one and have never used one or been stuck. If you get a flat, just drive to the next flat spot and change it. We have driven the mini van down Schaffer trail many a time for a quick day trip. You can do the entire trail in a day, but it's long. We do it on the motorcycles as a day trip or mountain bike it over 5 days.
Gotta stop at Muscleman Arch- hike a cross with the kids holding hands of course, then put them down, step 5-6 feet away, have your wife snap the picture of just the kids on the arch and use that as the picture on your christmas card. We did that one year and got a lot of calls from the family......Priceless.
As far as moab goes, the WRT is more highway than off road. It's beautiful, nostalgic, and a must do, but it's not a very tough trail. Heck- I ride it on my bicycle every year
You will have a great time!
PS- check out Pritchett Arch coming in from the south- it's a fun drive with kids too. There are lots of tough trails that start or end on the same road, so you can give them a whirl too.