I don't see a need to drive all the way south to Aqaba just to relax, then drive a few hours north to relax some more. Personally, I'd add a day to Amman, in part to recover from jet lag and in part for the Roman ruins in the area, and if you want the down time spend all of it by the Dead Sea. Nothing wrong with the previous poster's suggestion to spend more time in Wadi Rum, either.
(When you're in Petra, don't miss the ice cream at your hotel.)