The brace is pretty firm so I don't think you have enough mobility to do all the poses. You can always try it and if it doesn't work for your class you can send it back.
15-0951 Knee Support The attachment strap is attaches on the outside of the knee, (away from the other knee), but I do not see a place to specify which knee to order for my needs. (E.g., left or right knee.)
This brace does provide support for the MCL. This is an athletic brace so you shouldn't have any trouble using it for Taekwondo. However if it doesn't offer the support you're hoping for it is returnable even if you have worn it a few times