Hi OliverB,
just to clear up some distances:
Evason Ma'in hot springs is right next to Dead Sea - about 30 mins, by staying there, you do not really break up the distance to Petra as your driver would take the scenic King's Highway anyway and will require around 3 hours.
Madaba to Petra is still around 3 hours, Madaba, Dead Sea, Ma'in are all right next to each other.
Wadi Rum is an excursion to be done from Petra NOT from Dead Sea - about 1 hour. From Dead Sea it would be 3.5 hours or more.
Jerash from Dead Sea is OK, around 1.5 hours
So from a vicinity perspective you should consider those distances...
Here's what I was thinking:
AUG 25 - American Colony Hotel, Jerusalem
Don't know how long it will take to cross over to Jordan. You will have to figure this out.
AUG 26 - Kempinski Ishtar, Dead Sea
AUG 27 - Kempinski Ishtar, Dead Sea, visit Jerash, Mount Nebo and Madaba from here
AUG 28 - Movenpick, Petra, visit Wadi Rum from here
AUG 29 - Evason Ma'in Hot Springs, Madaba and Mount Nebo
Return to Tel Aviv
I must say, however, that with the distances involved, what you are trying to achieve in this short period of time is quite a lot.