We are dedicated Canon users on our household and I was in a similar position as what you are describing a couple of years ago and I went with the Canon Powershot SX 40. It has more functionality than a point and shoot without being as complicated or cumbersome as a full fledged SLR. It has an awesome auto mode if you don't want to think about anything but it also has a variety of other modes that allow you to have more control if you want. It has a sports mode and a rapid fire capability which from your post sounds like you would have lots of use for.
I have been thrilled with the zoom and that was one of the other things that I was really missing on my point and shoot. I also really liked that in addition to the built in flash you have the option to add a larger external flash if you wanted. However, thus far I have found that I don't need the flash very often at all.
Like I said the model I have is a couple of years old so you might also want to check into the newer versions of the same product line as well. This is the one I have:
And if you are interested in seeing pictures I shot with it on our Disney cruise/WDW vacation last month please let me know and I will be happy to send you a link. Hope this helps and happy shopping!