Buying a camera for the baby on the way and the two year old.

Babies have very small hands and weak muscles, so if you are buying a camera for one, a DSLR may be way oversized.

Kidding obviously

Everything I've read about the T3i says that it will be great for what you want. I went with the T1i because I am really only interested in stills and could get away with a lower price, but for video the T3i is supposed to be much better. I second the rec for the kit lens + 50mm 1.8. For a smaller subject like an infant or small child, the 50mm length on a crop sensor will do well. Also would recommend investing in a flash for photographing people. At minimum get one of the Kobre's lightscoops, but that will never match one of the speedlight flashes.