Andy-
While I completely agree with Grimace that the 70-200L is one the of the best zoom lenses ever made (I have the f/2.8 non-IS), given your needs I would seriously consider the advice that compuwar gave you. There are several reasons for this. For one- the uses that you described would not be quite met by the 70-200. If you're interested in doing birding, then the equivalent focal length of 320mm (200mm X 1.6 FOV crop) will indeed be awesome for sports, but will be in the low end for birding. The 100- 400 on a 1.6FOV crop is an awesome telephoto- going from a 160 to a monsterous 640mm. That will be more than enough to cover your birding needs.
My second reasoning is that given the recomendations for websites, you were undoubtedly dissuaded from the 100-400 by fredmiranda's website. One thing to keep in mind is that most of the people there are professional photographers, who really have all the time to measure the slight barrel distortion of that lens, versus the minute pincushion here... this is all stuff that the regular joe like us will never really care about, or notice. Fact is that on a crop-sensor camera, the 100-400 is an awesome lens. If you aren't planning on getting a 1D series, or a 5D ($4-8k, $3k, respectively), then you will likely not be bothered by the slight loss of sharpness at the corners on a full-frame camera (remember that with a crop sensor you're shooting in the sweet spot).
My last reason is price. The 70-200 f/2.8 IS is an expensive lens. On a good day, you can find one for about $1500. The 100-400 is about $400 less than the 70-200. That $400 can be spent on a number of things. You said that you don't feel the kit lens is enough. For $300 you can get a 50mm f/1.4 lens, which will allow you to take some awesome portraits of your kids. That kind of money can also get you a nice flash- yeah, the XT has one built in, but if you're doing any sort of stuff where you're far enough away (and with a 100-400 you might be), a nice solid flash, like the 430EX ($240) would be useful.
Just my thoughts. Someone will probably disagree with everything I've said.