Efrem

I've never been to Lebanon, so I can't comment on that part, but you're trying to squeeze a whole lot of Jordan into those four days. For starters, you could drop the Dead Sea from day 3 unless there's something specific you want to see or do there. It's south of Amman, while Ajloun and Jerash, which you have on the same day, are near each other and to the north. You'll be much closer to the Dead Sea when you visit Mt. Nebo/Madaba on your fourth day if it's a must. I don't think one day is enough for Petra either, but if that's all the time you have, it's better than nothing. And too bad you'll miss Wadi Rum ... Nothing against Lebanon, but have you considered leaving it for another trip?