Hey -
I went on a plane trip with my children and I actually downloaded a couple of Dora episodes onto my ipod. My daughter loved it and it definitely occupied her. They were $1.99 each, I think. Also, I now have an iphone and she really likes Tozzle. They have a free version, but it doesn't have very many puzzles, so I went ahead and paid the $1.99 for the puzzles.
As others have said, when you get back from your trip, the kids will want to continue to play with these items. I just told them no. And now, they have no expectation of using my ipod at all. I do let them play with my iphone still, but it has to be at a specific time (in the doctors office, late in the evening, etc. It's not just willly nilly at their demand).
There is also a free toy story ap which is a matching card game. My 3 year old loves it, but I am not sure how a 2 year old would do with it. Oh, and "Make me a princess" - free ap to dress up a princess. You can even take a picture of your daughter and then she can dress up herself. My daughter loves this one as well.
Good luck!
L.