Wonderful photos mate. We didn't go up as far as Amman. Based ourselves in Aqaba as flights were in and out of there and then spent a night in the desert and a night in Petra (Wadi Musa). It wasn't too bad for tourists, I think most of the websites advise to go from March due to the weather, as it was pretty cold before the sun had risen - but still a beautiful temperature during the day and 23 down in Aqaba. You can't really put it into words, my wife is so good at just taking the plunge on these things regardless of kids and I'm so glad we did.
Did you walk up to the monastery? My 4 year old walked the whole way from the site entrance up to there and back which was incredible on his little legs, and really useful considering we had to carry our 1 year old for most of it and my 5 year old also gave in on the way back down!
I echo your thoughts, particularly with Easyjet flying direct to Aqaba and a hire car costing about £100. 1hr drive to the Wadi Rum and another hour up to Petra from there so it's really accessible and not too expensive considering it's a wonder of the world.
Aqaba definitely a good position to base yourselves in, particularly with the cheaper flights via Easyjet (though Wizz Air now serve Amman from Luton at a fraction of the cost of BA/Royal Jordanian from LHR.....if you can stomach Wizz for 5 hours!)
Aqaba is a bit more accessible for Petra and Wadi Rum too, though you're never too far from anything in Jordan.
I didn't quite have time to do the Monastery....I could have possibly squeezed it in had I rushed it but the weather was boiling by this point and doing all them steps in the early afternoon sun wasn't super appealing.
Very impressive your 4 year old managed it, fair play to him as it's a fair old trek from the entrance.
It's a fascinating place for us adults so I can only imagine what it must be like to witness Petra at 4/5 years old, incredible, very lucky children indeed.
I guess that's an excuse to return as I would like to see the Monastery, and also do the hiking trail to get the elevated view of the Treasury.
Also quite fancy doing the 'Petra by night' they offer on certain days, so it'll be on the agenda to return at some point in the future and to stay at least one night in the immediate area.
Assuming they still offer the route, I'll likely use that Easyjet service in/out of Aqaba to also tick that box.
I'd go back tomorrow if I could :(