I've used all three lenses discussed in this thread (85/1.8, 100/2, and 135/2) to shoot gymnastics.
The decision of when to use which was based mostly on the focal length needed for the situation. Occasionally, and especially with older digital cameras (of more than 10 years ago), the limited light would force me to use the 85/1.8 even when I would have preferred to use the longer focal lengths.
The 1.8 made a difference. Some respondents here have dismissed this difference as negligible. That may be true with the higher ISO capabilities of cameras today, but with cameras that introduced distracting noise at any ISO greater than 1,600, the 1.8 was an enabler where smaller apertures failed. Nowadays however, with cameras producing relatively clean files at ten times the ISO (eg. I've shot at 16,000 ISO recently) the difference between 1.8 and 2.0 probably is negligible.
With the newer cameras (specifically the 1DX) I rarely use any of these primes to shoot gymnastics anymore (although I still have them in my bag), because the 2.8 zoom is so much more efficient at reframing the action shots. I hear that the 7D2 is good up to 6400. In that case, I would still use primes to keep the shutter speed higher.
Your best bet is to base your decision on your access to the apparatus during competition. If you have close access, then definitely get the 85/1.8. Images with cropped off body parts just don't look right. Even if only a few toes or fingertips are missing, the shot looses something, unless really cropped in tight. Even then, it is best not to chop off the hands, as the shape of the hands and fingers are expressive and communicative, like facial expression. We view the athlete's strength, tension, grip, poise, por de bras, dance, and action by mentally, even if subconsciously, observing the hands.
If a longer focal length forces you to cut off those hands too often, it is better to choose a shorter focal length if you cannot step a few feet further back without a coach or another athlete or another parent passing between you and your intended target (which invariably happens right at the peak moment).
No need to base a decision on what the lens barrel is made of. The barrel doesn't make the picture. It's the optics and the aperture that puts the light on the sensor.
You can't go wrong with either the 85 or the 100 as far as optics (they are very similar) are concerned, but you also can't make the hole behind the 100 as big as the 85, nor can you easily rebuild cut off fingers and pointed toes in Photoshop for every frame either. On the other hand, if the 100 will put more pixels on your kid, given the distance you are limited to shooting from, then longer will make more sense.
The point is, the choice is better based on your shooting situation, not a forum fed lens reputation.