I would recommend that you choose either Jordan or Israel, or reduce the amount of time in the Dead Sea.

4 and half hours in Petra is not really enough if you want to do it properly. I spent 1 and half days in Petra and for me that was only just enough to walk around the site, climb up to the Monastery etc.. Personally, for me 2 hours in Wadi Rum was enough. For the Dead Sea I would recommend one night, two at most. There is really nothing to do there (unless you go to Masada). It's unbearably hot for most of the day, and once you've floated in the Dead Sea you've done it. I've been many times, but never for more than for a day trip with friends/ family. By 1300 it's too hot and you either have to sit in the shade or sit in the hotel. I found (as a young 20s athletic male) just walking outside the hotel to the car and back unbearable when I was there last June.

I would suggest that you increase your time in Israel and use some of the time from not going to Jordan/ less time in the Dead Sea to visit Jerusalem. You could fly into TLV on easyJet on Thursday, spend a few days in Tel Aviv, then go to Jerusalem on Sunday, one night in Jerusalem, and then take the bus/ a car from there down to the Dead Sea. Going to Jerusalem on Friday/Saturday would not be worth it due to Shabbat.

If you do go to Jordan be prepared for security in ETH. I've flown internationally and domestically from TLV, SDE, ETH airports numerous times and security in Eilat has always been a lot more time consuming that at any of the other airports.