Lens for shooting outdoor acrobatics ?

The answer to what you are looking for is fairly complicated so this is going to be quite a long post.

There are several situations to consider:

1. Videoing acrobatics.  For this you don't need a fast shutter speed because it is determined by the video fps rate, so a "fast" lens (small f/ number) isn't necessary.  If you are hand holding, OIS (image stabilisation) is certainly necessary and neither the 20mm f/1.7, nor the 25mm f/1.7 nor the Sigma 30mm f/12.4 have it.  If you want to change focus during a video clip then you need a fast focusing lens and one that focuses silently so that the focus noise isn't heard on the audio track.  I am not familiar with the 25mm f/1.7 but the 20mm f/1.7 is both slow focusing and noisy.  So, overall,the "prime" lenses that you are looking at may not be as good as the 14-42mm lens that you currently use.
2. Still shots of acrobatics.  A "fast" lens will help you to freeze motion if that is a current problem and OIS is not an advantage because you need a fast shutter speed anyway, but fast focusing will be very important.  So the 20mm f/1.7 is out but I don't know about the 25mm f/1.7 or Sigma 30mm f/1.4.
3. Indoor shots of moving subjects, including children and people.  A fast lens like the 20mm f/1.7 or 25mm f/1.7 will be good for these, but an external flash with a head that can be tilted up to bounce off the ceiling may well be a cheaper and better alternative.  It will be the only alternative in really low light.  External flashes can be very cheap and the image quality if you bounce the light off the ceiling is excellent.
4. Outdoor shots of moving subjects in low light.  You can't bounce the flash because there is no ceiling so a fast lens would be a good solution.
5. Indoor or outdoor shots of stationary subjects in low light.  Holding the camera steady become the main problem as a fast lens would be useful but, if it doesn't have OIS, it may not be as good as your kit lens with OIS.  The other alternative would be a to use a tripod.

So, lenses like the 20mm or 25mm f/1.7 may not be any better than your kit lens for your acrobatics video, but get advice from other people on this forum about using them for this kind of video.

Still shots of acrobatics are likely to be tricky because you need fast focusing and the 20mm f/1.7 won't be good at that.

Lenses like the 20mm and 25mm f/1.7 will be good for shooting people in low light and that is what I use my 20mm f/1.7 for.  However, indoors a flash may be even better.

I am sorry that I can't simply say "get this lens and use it for everything" because unfortunately a simple solution like that, e.g. the 12-35mm f/2.8, just isn't possible within your budget.

I hope that somebody else may be able to come onto the thread with a different solution that I haven't thought of.