What if you promote yourself as a holiday helper? You could babysit during this holiday time, or bake for others, wrap presents, clean houses, etc - just for the next 30 days or so, if that's all you think you can do.
That's a good idea. The Y here has a program during the holidays where you can drop your kids off in the nursery for up to 4 hours while you go shopping. If it sounds like something you'd be feeling up to do, post some fliers around base like that, drop-in babysitting services for up to 4 hours and give certain times they can come.