Congrats on wanting to upgrade. This is a big step .. going from a P&S to a DSLR. I did what the pp said .. I felt both cameras in my hand. I tested the Nikon and the Canon. They both felt great and they both got great reviews. The only thing that I noticed was the there are more lenses compatable with the Canons and they are cheaper. That is the only reson why I went with a Canon. I bought the XTi in 2005 and lastyear I bought that XSi .. love both cameras. The picture quality is amazing.
As for the action shots of your kids,this will take time. Read your settings and you will doing them in no time. I got to shoot the Baseball All Stars and got some great shots. Even went to a Reds Baseball game and got some cool action shots there also. The best way to try your hand at actions shots .. from my take, is to have your kiddos jump in the air. Once you get them in the air and get great shots .. you will be snapping pics. like a pro!