Hi, it's been many years since I was braced so I'll wait for other people to chime in with more up-to-date info, but please don't worry about your daughter's gymnastics Karis. She will almost certainly be able to continue with this and will be allowed to remove the brace whilst doing so. Having a strong back is a very very good thing
As to which brace is best - there are many, many different opinions on this. I would simply advise that you follow the advice of your daughter's consultant. There are a handful of charlatans out there who sell braces privately, so be careful of this. The "standard" type of brace prescribed in the UK is a custom-made TLSO; this is a hard-plastic corset-style brace. It is similar to the Boston Brace, which is also commonly prescribed; the difference between the two is that the Boston is constructed from prefabricated parts rather than being custom-made from a plaster cast of your child's body.
You may also hear about the Spinecor brace, which only a few NHS hospitals provide; this is made from fabric bands so it is more comfortable to wear and allows for more movement, but the jury is out as to whether or not it is an effective brace.
The Milwaukee brace is still used very occasionally for children with very high thoracic curves. Modern designs are much nicer than the old style Milwaukees but this is still seen as a tough brace to tolerate and so it has fallen out of favour with most consultants.