Travellingstudent - thanks for the prompt reply and valuable insight. I have actually already been to Israel and visited Jerusalem. Sorry should have been clearer on that. The only place I didn't go was TLV. Mum is doing a pilgrimage before I meet her that is fairly gruelling hence her wish to chill out at a Dead Sea hotel & spa for 3 nights. So yeah it will be boring and hot but hey-ho if that's what she wants...!
Wadi Rum I am really just staying overnight at in a tent then doing a 2 hour Jeep tour in the morning...
So based on what you're saying it's really whether I add some time in Petra...but that eats in to TLV. Food for thought.
Thanks again.