@farbster: I did actually hire an award service for my next summer vacation, which is not a heavily-traveled place: Vancouver and Anchorage. They are still looking for my desired dates but I do think they are having a hard time finding 4 tickets available all together in the same flight.
I have miles in many different programs so I am relatively flexible, but I would like to use a combination of them so I don't lean too heavily on United. After all, collecting miles for 4 is also a lot harder than collecting miles for 1 or 2.
I feel I have also looked into departing and arriving at different airports to include flexibility and it's still hard. But I will start looking at more regional airports, such as Philly and Boston.
I really like some of your ideas to split the party to travel with different alliances but from the same airport, but within similar departing and arriving times. I feel very comfortable traveling with one kid or both. My husband a bit less so. I think this thread gave me great tips about splitting the party, maybe 2 and 2, or 3 and 1.