If only this were 2011-12; I had a bunch of United systemwide upgrades I never used...
Forget about upgrading/using miles for C. Kids probably won't fully appreciate it anyways, even if they're teenagers. Gold on AA doesn't get you lounge access IIRC; you need Plat for that. Also it's not THAT long a flight compared to starting further west in the US or going further east in Europe. $2700 doesn't sound jump-on-it-cheap for C on IAD-BCN, actually. I'd hope for low $2000s.
Would look for nonstops out of IAD over cxns anywhere. You should have nonstop options on multiple airlines. Not having to deal with changing planes/missed cxns on intl flights is a big deal, especially with kids. Also, when returning to the US, I hate having to get on another plane after a long flight and clearing customs.
The premium coach option is compelling. European airlines can be stingy with awarding miles on the cheapest fares, but you're probably buying a few fare classes up from the bottom. Check the fare class and mileage awarding rules if this matters. Also sign the kids up for the miles programs if they're not enrolled already. Other than UA E+ the only "premium economy" I've actually flown in is SAS's, but it was very agreeable. That was back in 2003 I think; ever since then all my intl flights have been up front.
Generally the lowest summer fares post in Jan/Feb, so you should probably have a few weeks, but I wouldn't go too far past mid-March. There have been exceptions to this during recessions (2009 summer airfares stayed obscenely cheap all summer). Also act fast if oil prices shoot up.