Having traveled in the middle east and in Africa, I would suggest leaving nothing to chance. I echo what was previously stated. This is a different part of the world and you want to make sure that everything is in order.
 Even if everything is in order, there can be problems, they are trying to shake you down for dash (bribe as it is known in Africa).  
There are lots of things to do and see in Jordan and Israel, it will be a great trip, but leave nothing to chance.

You should leave nothing to chance, it is hard to predict what will happen at the Jordanian/Israel border. Expect to be interrogated on your travels in Jordan, who you saw, who you were with. Israel (for many good reasons) is extremely cautious about who enters the country and can delay you no matter what visas or other paperwork you might have. I have traveled to Israel on more than one occasion and have experienced trying to enter from Jordan. It is doable, just be patient and respectful.

You should go downtown and get a 2nd passport. If you had asked early enough I would have recommended one of another country if applicable.

I just made this crossing (both ways) recently. If my experience and the experience of many of my friends who did the same is any indicator, it was pretty easy. I would not anticipate any problems. If you'd like to troubleshoot potential issues or if you have any questions, please feel free to email or chat me, though!  Are you flying Royal Jordanian from O'Hare? It's non-stop!

Could you fly from Israel to Jordan and avoid the border?