I have neuphues that age, and have had the same problem.
Croyal makes a "plug-n-play" colouring game perfect for kids as young as three (of course it is for the TV) (and as cheap as $10).
As far as DS games for three year olds, hopefully someone else can better help.
Probably there are some GBA games that might be best for a young child (sponge Bob, Dora the explorer) and these WILL work with the DS.
ALSO, you can GBA videos... although not techincally games, this should atleast help the three year old not feel left out.
