re: 20hr layover in Dubai or Doha?

Don't take Qatar to Doha. Active, and blatant support for terrorists.

What about Abu Dhabi? The Ritz there is about $250 a night, but it has a great pool setup, with a graduated wading area that would be good for the younguns. It's much less "Arab bro" than Dubai seemed to be. It also has Yas Island, which (I'm pretty sure) has a waterpark, it has a go cart track, etc., but your kids aren't really old enough to really care whether you're at the hotel pool or a waterpark.

It's the only hotel I've every stayed in whose air conditioning worked so well, I managed to create condensation on every hard surface in my room by the time I woke up. I have a practice of jacking the AC down as low as it will go. In the US/EU, setting it at 60F means it may hit 68. At the Ritz in Abu Dhabi, if you set it at 55, you got damn near close to that.

For navigating the experience, we probably need to know departure and arrival times for your options. Some will suck far worse than others, particularly for you, the wife and the older two kids. Dubai seems like a big pen1s swinging exercise on buildings and cars. Abu Dhabi, families come out after sunset to BBQ and go to the beach.

But you only have 20 hours, so it's not like you can add a ton of stuff to your list wherever you go.