I had this same dilemma many years ago... with the original digital rebel.
I'll echo some of the other thoughts you've had on here. The 85 1.8 will be a big step up in terms of low light performance- somewhere around 2 stops or more better than your longer zoom. The reach is not ideal, but indoor fields are typically much smaller than outdoors. With the crop sensor body that you have, you can make that work.
My path was to try the 50mm 1.8 to see if that was workable. It was, but that's a pretty low end lens. I felt the 70-200 was priced way out of my reach at the time, so I bought the 85 1.8. Not quite enough reach for me all the time, so I bought the 200 2.8 (the prime, not the zoom). This was my first L lens, and I really thought it made a big difference in my photos. With the camera I had though, even 2.8 wasn't ideal indoors- I had applied a hack to the camera to increase the iso to 3200... but that was still noisy on that camera, and not giving me enough light to shoot action sports at higher shutter speeds. So... I tried the 135 2.0. Another great lens, but had it's limits.
In the end- I was never 100% happy until I did 2 things- 1- get a camera that handled higher ISOs better. For me, at that time, it was the 40D. Then- I gave up and finally bought the 70-200 2.8 lens and began to get the photos I wanted.
So that's a long story- sorry about that. My lesson was... I should have just sucked it up and bought the better gear from the start. I now have 50 mm, 85mm, 135mm and 200mm lenses that rarely get used. The 70-200 that I resisted buying because of the price is easily my most used lens. I would have saved a lot in the long run to just buy it from the start.
Your camera, btw- probably has higher iso settings than mine did. My guess is that although they are both entry level, yours will be far better at higher isos than mine was, just from the advances in technology.
One last thought- I have been reading a lot lately about the fact that in-camera noise reduction (which only works for jpgs) is far superior to anything you can do in post processing. I haven't really tested this side by side for myself yet, but after shooting for decades in Raw, I have started to shoot soe of my high iso stuff in jpg. So far, I can't argue with the results.
Good luck with whatever you decide!