I would choose Beijing without doubt. I've been to the city a few times and loved it. It'll be a great experience for your dc. Yes the air pollution is an issue, but you'd have the same in HK, for example.
Miami gang violence, crime and weather would not be my cup of tea either.
I don't know anything about Abu Dhabi, but sagacious, I second you. Expat compound living would definitely scare me off. Might as well go to Gran Canaria into a share time condo like ze rest of ze Germans... One more thing re expat compounds being safe: so all the foreigners are huddled together in an artificial village with national (local) protection. Has anyone seen the movie 'The Kingdom'? It is based on the real story of a massacre taking place in Riyadh years ago. www.telegraph.co.uk/global/main.jhtml?xml=/global/2003/11/28/wbush128.xml FWIW, I wouldn't want to live on the Arab Peninsula and I have a middle Eastern name and the accompanying looks.
Beijing is rife with history, great food, fab nightlife and things to discover. You will be able to afford a helper and travelling on the tube is not tricky once you decode the colours. Lots of expats there, too and the hinterland has lots to offer in respect to historical buildings (Great Wall), artefacts, temples, breathtaking landscape, villages, etc. If you have the chance to go and it's not permanent, then I'd go for PEK.
Make a list of priorities, what is most important to you and then apply it to the 3 cities. The one which meets your criteria the most (close to home=Abu Dhabi, same lifestyle, better weather= Miami, etc)