Don't do BA. Most domestic airlines give you 100% miles for any ticket bought on the airline or partner. BA gives you a % of miles, so you may get 50% or nothing for some asian carriers. The family account is nice only if you travel a lot internationally as a family on OW and still you have to get a certain class of fare which often is much more expensive.

Business - If I remember, the firstclass flyer.com site compared business accounts and found the best bang for buck with NW and DL.

Best is to fly and once you get to 5k for the kids combine their miles with yours. The airlines charge 1c / mile to transfer and add a fee. Watch for the times during the holiday season when you can do it fee free. Think of it as buying miles for half price. usual limit 15k united, no limit US (had 40% bonus last year), 150k for DL (they often have 100% bonus as well)