The main issue with Petra and Wadi Rum tour actually in winter time in one day is timing itself , and it might be difficult to do because: It takes 3 hours driving from Amman to reach Petra .
Petra site is huge and the minimum recommended time to spend on the site is 4 hours (Some people spend full day in the site from sunrise to sunset ) , Driving time from Petra to Wadi Rum is 2 hours, The minimum tour time at Wadi Rum is around 2 hours ( Jeep Safari tour ). Sunset time is around 04:30. Saying this , and even if you started from Amman early morning at 07:00, reach Petra at 10:00 , take the tour and leaves at 14:00 , reach Wadi Rum at 16:00 - no enough time to make even the Jeep tour at Wadi Rum..
We usually cover Petra and Wadi Rum in two day tour and spending the night at Rum vallely as well, saying all this however; it would be possible during summer time, where sunset time at Wadi Rum is around 7pm.