OK, shame they'll miss out on the fun of doing the land border crossings to/from Israel both north & south
I would recommend looking into the Jordan Pass, worthwhile to get and saved us a lot of money.
I would suggest something like:
- Pickup car, go to Jerash (ancient ruins) and then head down to Madaba - spent the night there or if they're whizzing around quickly enough then goto Mount Nebo and continue on to stay at one of the resorts on the Dead Sea
- Chill day if staying at a Dead Sea resort property, otherwise if staying in Mabada or similar then head out to the Day Sea and just do as a day trip (depends on how much of the experience they want to do; some like to do the whole hotel/resort thing.... Mrs FB and I didn't and instead opted for this fun way of doing it Dead sea free swimming · 65, Jordan - much more adventurous way!)
- Head on to Karak and do the castle (optional, but was a good stop - if in a rush then bypass and just go straight to.......)
- Petra - you'd want to spend a full day here, make sure the hike up to the Monastery is done. It's long, hot and all uphill but worth it once you get to the top. We spent about 6-7 hours there, unlike some tourists who simply came in, saw the Treasury and maybe had a little further wander then left....... waste. Entry is covered by the JP, too which just about pays for itself completely (ignoring that it also covers a Visa into Jordan, Jerash, Karak Castle, etc.)
- Overnight in Wadi Musa or somewhere close, or push on down to Wadi Rum
- If pushing on then spend 2 nights in Wadi Rum - spend the first just arriving/chilling then on the next day do a whole day jeep/hike tour; either that or opt for a half day jeep tour. We used Wadi Rum Fire Camp who were really good, cheaper than the rest and also included lunch when doing the half day tour. I can put them in touch with Ibrahim if they like.
- From there either a big drive back up to Amman, or..... have a look at the Jordan Pass map and find some points midway and stop overnight and meander their way back up.
Happy to jump on the phone and have a chat with them also if they have any questions.