I have been using Macs since... well... since Performa computers, Mac VI, purple iMac with hokey puck mouse...
Currently we have:
iMac 24
MBA 13
iPad 2
2 x iPhone
one dead MBP 15 replaced by work's MBP15
For what it's worth as d@rk51d3 said I would not use the MBA as a family computer. It has power, true, it's energy efficient, true but the solid state HDD is small and I would argue that the MBA might be struggling with external monitor and a number of user profiles. It was designed to be ultra-portable with long lasting batteries and solid state HDD to extend battery life even more. It is not meant to be a light-weight substitute for MBP.
We use the iMac as everything, wife is using her MBA for whatever she needs including business travel, I work on MBP and use the iPad for travel and email and whatever I want. We travel with the iPad as opposed to MBA for two main reasons : built in GPS and WiFi/3G network (in NZ we just bought a sim card and we were off and running connected to the world in 5 minutes - you can connect the iPad to a camera as well to download your pix).
Previously we used the MBP for everything and it was great before it's death. We had it hooked up to an external monitor, mouse and keyboard and it was fine. So unless you really need a very portable computer I'd go for MBP as it does have more grunt and bigger HDD and (I think) more video RAM to run external monitors and the like. Bit heavier but more grunt.
As for kids not using it for games... well it will change and even the online stuff my 8yo plays (MoshiMonsters, Club Penguin...) they will soon get used to the performance and need more.
To be honest I'd suggest an iMac (we got ours refurbished) as a communal computer and MBA for YOU. I am of the opinion that MBA and MBP are truly 'personal' whilst desktops are, well, communal. On the other hand, iMac and iPad are a good combo as well. My iPad is MINE. It is personal and I do lots of emails and surf the net on it (and watch iView). Yes, it does have games for the kids, but it is mainly my personal assistant.
My sister (who was converted by me) has 2 x iMac, MBA, 2 x iPad, 3 x iPhone and my brother in law now has MBP for work and Apple TV. Totally Apple household. The iMacs are communal, the laptops are personal. works well for us and her.
Anyway, back to AngryBirds ;-)

