It depends on your needs. If you are just taking photos of the kids and can't move around then I'd probably go with the 70-200 2.8. I used it for three years for indoor and outdoor sports, and you can get usable results indoors with good post-processing unless the lights are terrible. The 70-200 F4 is useless for indoor sports.
However, if IQ is what you're after the 135 L is infinitely better than the 70-200 2.8. I just received my 135 L two days ago and the results aren't even close. It is much, much sharper and you can shoot at ISO 800 indoors with decent lights. It is a bit long on a crop camera though, but I'm making it work so I can have a bit extra reach at night outdoors.
Here's what I did. I sold my 70-200 2.8 (just wasn't happy with IQ at 2.8, not good enough for publications) and with the money was able to buy the 135 L and the Sigma 100-300 F4. I use the 135 indoors and will couple it with a 1.4 TC for a 190 2.8 which I can use outdoors at night. (Buy the way, the 135 L coupled with the 1.4 TC still gives better results than a 70-200 at 2.8.) The Sigma 100-300 is a terrific daytime outdoor sports lens on a crop camera and has given me great results so far.
Just a suggestion, there are a lot of good lenses out there and certainly more than one way to go.