It was a tour, but a 3 day/ 2 night one from Jerusalem run by Abraham Hostel. It had one full day in Petra, which I really think is the minimum, plus we stopped at Jerash and Wadi Rum!
I basically saw those day trips and immediately concluded they were a terrible idea, and recommend the one I did to anyone who is short on time but wants to see some of Jordan while in Israel. It was a pretty classic "backpacker tour," so nowhere near as organized as most of them but organized enough that you could see more than you would in a short amount of time.