Apologies for the similarity of this thread to some others but I did not want to hijack other people's threads.

I am taking my mum to the Dead Sea for her birthday on set dates in October (Sun 21st to Wed 24th). I am taking the opportunity to do some sightseeing before. The elements I am most interested in are Petra, Wadi Rum and Tel Aviv. I have to do this before the Dead Sea visit and can only take 2 days off work so the earliest I can fly out from London is Wed 17th evening. There is a RJ flight LHR-AMM which i can use Avios on to reduce the price from £440one-way to £190 taxes. The return is a miles ticket TLV-LHR on BA.
So what to do between 17th and 21st. Here is an itinerary I have put together partly using Dakkak Tours who someone else on this forum recommended. I am keen to know from people who know the region whether this seems an effective use of time. And budget!

Wednesday 17th
17:00-00:00 RJ Miles flight to Amman: £195 + 12,500 miles
Night at Crown Lounge bedroom: £30

Thursday 18th
07:00-10:30 Morning seeing Amman
10:30-14:00 Meet driver for day and go to Petra
14:00-18:30 Tour of Petra
18:30-20:00 Drive to Wadi Rum
20:00-23:00 Dinner, entertainment and night in Wadi Rum (all above £270)

Friday 19th
08:00-10:00 Jeep Tour of Wadi Rum £30
10:00-12:00 Drive to Arava crossing £20
12:00-13:00 Border formalities
Taxi Arava to Eilat airport
14:30-15:30 El Al flight ETH-TLV: £40
17:00 Checkin to TLV hostel

Friday 19th to Sunday 21st
Two nights hostel in Tel Aviv: £50

Sunday 21st to Wednesday 25th
Dead Sea

The other options i'd considered was an Easyjet flight to Amman on Thu 18th and packing in Petra and Wadi Rum in a (gruelling) day on Fri 19th before using miles to fly onto AMM late on the 19th. But aside from the discomfort of flying Easyjet for 6 hours that allows me little time in Petra (~2hrs) and Wadi Rum (~2hrs). Which somewhat defeats the point

Finally I could also just sack off Jordan and fly to TLV using Easyjet on the Saturday. Thus saving about £400 on the above itinerary. Keen to hear if anyone thinks Jordan is not worth it. Though from what i've read I doubt this will be the case!

Thanks in advance for any feedback.