You will not be able to combine US and UA mileage balances.

NOTE: I'm assuming that you aren't doing a lot of flying so your mileage balances won't change much from the "normal" way: taking paid flights.

The UA Visa offers a 15,000 mile sign-up bonus for a $60 annual fee. That plus a quick switch to Sprint puts you right about at two free tickets on UA. (Use iDine to bump up to 70,000 if you need to. Also use iDine to goose your DL account - it's amazing how easy it is to pick up 5K or so over a couple of months.)

For the 4th ticket, you can either work on that US Airways balance by signing up for the credit card, doing iDine, and participating with their other partners, or you can just decide to do one paid ticket with the three free ones. Depends on how aggressive you think you can get to add 20K+ on US in addition to topping off DL and UA.

Since there are 2 small kids involved, you will probably want to book all four at the same time (because you can't change the names once you've ticketed) - either 3 UA 1 DL or 2 and 2 like you mentioned. Therefore, flexibility to pay for one of the tickets may make things a lot easier for you.

Another idea: once you reach the level where you have 3 free tickets, you might consider subscribing to AwardPlanner. For $49, you can tell them your situation, available awards, and have them do the legwork for you. They will come back with what's available, the fare for the 4th ticket (if paid), and lay out the options for you. No hassle on the phone with UA, DL, and US for you.