[molsongolden]

Have you tried Love Letter?

http://boardgamegeek.com/boardgame/129622/love-letter

It's dirt cheap and many people create their own custom themed version. I have a super mario love letter clone deck that was printed via an online service and it's great. Your young kids should be able to pick it up and it's playable with 2 but good with 4.

[karlb]

I bought Love Letter based on your recommendation, and both kids—and both adults—love it. We have played it twice a day since we got it. My five-year-old daughter doesn't really understand it, but she enjoys being on a team with someone else.

I found the user guide painfully confusing, especially considering how simple the game is. The mechanics of the game are shoehorned into a game theme that barely makes sense. In the end, all four of us watched the following video, stopping once we had got the idea: https://www.youtube.com/watch?v=hX-Du4P_FME

One advantage of Carcassonne is that my five-year-old can play on her own, because the game is "open"—it doesn't depend on players hiding their cards from other players. So whenever it's her turn, we can help her to decide where to place her piece.

Please let me know if you have any other recommendations for family games.