We had a limited time to visit Petra from Israel and saw the border controls could be tricky and time consuming.We were going to hire a car but couldn't take it in to Jordan.
So we got in touch with Mohammed of Classic Wadi Rum tours and he arranged a taxi in Israel and Jordan and walked us through customs on both sides of the border. We arrived that morning in Tel Aviv got through the border at Eilat and spent a few hours in the beautiful Wadi Rum where Lawrence of Arabia was filmed.He got us to the Marriott hotel in Petra before the evening meal and gave us a private tour guide to visit Petra the next day.Loved it ! Always wanted to go there.We wanted to return to the Sea of Gallilee by the evening of the next day.He organized a taxi up to the border crossing at sheikh Hussein at the northern end of Jordon and we were collected by another taxi on the Israel side.Bit of a tricky trip as his taxi wasn't allowed to take us directly to the border crossing and we had to take an free taxi to the border and walk ourselves through but By traveling up through the Jordan side we saw the other side of the Dead Sea and saved 4-5 hours by driving this way rather than going via Eilat.
We'll done Mohammed for a most enjoyable holiday!