Just got back
I just got back from Tel Aviv, Jerusalem and Petra last week. Loved every minute of it. I have been around the world and Petra has got to be one of the best places I ever saw. That said. Petra is a big place. We saw it in one day - from 7 am to 4:30 pm with nothing more than a bathroom break. So, if you are not quite as ambitious, you could easily make two days of it.
Here is how we went, I don't know if this will help you or not. We rented a car from Jerusalem to Eilat (Have to use Eldan Rent A Car - the biggest car rental in Israel, because all the other car rental places have a three day minimum to drop off in Eilat.) Stopped at the Dead Sea and Masada on the way down. Dropped the car in Eilat. Took a taxi to the Arava Border. Went across no mans land. Got a taxi on the other side directly to PETRA ($35JD). Stayed at the Movenpick (great rates at their internet website - wonderful hotel and right next to the park entrance.)
We arranged with our taxi driver going down to pick us up at 7:30 am two days hence. Believe it or not, he was there. Took us back to the border (1 1/2 to 2 hours). Walked across the border. Israeli border people called us a taxi. About 10 minutes later got the taxi. Took it to the car rental. Picked up car to TLV. Used to car for two extra days to see the sites in Northern Israel.
It sounds complicated, but it all worked smoothly.
The only complication is making sure that you have Israeli scheckles and Jordanian Dollars. DON'T make the error that I did and try to pay for something in Jordan with scheckles or try to change one for the other. They don't appreciate it. Changing your money and getting Jordanian Dollars can be a hastle.
If you would like more information. I would be happy to help.