ok, here's where i do have some knowledge, as i currently own both
70-200 f4 L, great lens, light weight, sharp as a tack, can be used with the canon tc and reatains auto focus,
cons, no iso, although supposedly sharper than the iso version, white, draws attention in a crowd, max aperture is f4, so not so low light
70-200 f2.8 L IS mk2, wow is all i can say, this is one sharp lens, and the new IS is really 3 stops handheld difference, this is what i go to for motorsports, and low stage light concert work. let's face it, sometimes only f2.8 will do
cons, this beast is heavy, i am not looking forward to working the bluegrass show all day with this one, i may alternate between the 2, go over to f2.8 for after dark
there are 2 alternatives i would suggest you consider, especially if you can make these focal lengths work for the kids stuff
the 135 f2 and the 200 f2.8, both are outstanding sharp primes, both can be used with the 1.4 tc, and still retain reasonably fast aperture, the 135 makes a great portrait lens if you can back off enough from the subject
and the best news is that both can be gotten used in excellent shape, combined for not much more than the cost of a new 70-200 f4 IS, and probably less than a used 70-200 f2.8 IS first generation. yes you could also get a used 70-200 2.8 first gen IS, but you have a as much weight as the newer model. and the mk2 is a real improvement. something to consider if yiou think you might ever go full frame.
don't forget, quality glass, taken care of holds it's value, and is good for years of use, you have a good body now, i would respectfully suggest starting to think along the lines of now building up a set of high end glass