I agree with the above posts recommending independent travel. It's easy.
I flew into AMM. rented a car and drove to Petra. It can be an awesome drive, passing a couple of Crusader castles (well worth a visit). There are two different roads and you can go south on one of them and return via the other.
You can spend the night in Petra (there are a bunch of international hotels).
There are lots of local guides offering their services. You can even travel to and/or from the site via a horse and buggy.
Enjoy