I always take pics of the kids around their birthday. I have a frame that holds one from each year till age 18. They are turning six in two weeks and we will be at Disney. I have the 24-70 2.8 but have been torn on a prime for the shots since I will be down there I do not want to bring tons of lenses. I am stuck on either getting a 50mm 1.2L or the 85mm 1.8. I want it to double up as a lower light or dof isolation lens on the trip also since my 24-70 stops at 2.8. This will be used when I get back for portraits. Just torn on the 50mm vs. 85mm. I do like the background creamy and smooth but sometimes like the one I took last year had some kewl Disney balloons from their party that helped capture more of the scene and what they were into at the time. I have a friends 85mm and notice it's definitely not as sharp as my 24-70 to be expected and the CA is slightly annoying but can be fixed in post. Also I looked at the 100mm macro and 135mm f2 for portraits but unsure if that's too tight indoors or at some of the places we go since the kids are little we do not let them stray far. Sorry I just need to make a decision and would like any suggestions.
In the situation you mentioned, I'de shoot for the 24-70f/2.8 II, great Lens, you wont be disappointed I'm sure, and in the Disney outdoor environment the Zoom will be in a class of it's own.
The 85f/1.2 L II is also an excellent Lens for this sort of portraiture, but it's more of a scalpel, precise sort of Lens.
And if you want to give your subject more room, less in your face when taking Portraits, the 135f/2, sharp as a razor & not as expensive as either of the two mentioned previously.
I use all three dependent on conditions, the 24-70 gets the vote for flexibility though along with great IQ.