Yes, they complement each other. I also practice taekwondo and yoga. In fact, the most important thing in taekwondo practice is not strength, but reaction. To be fast, the power it needs is also the power of speed. Flexibility is very important if you want to practice Taekwondo well. Without certain flexibility, you can't practice Taekwondo well.

There shouldn't be a pavilion where taekwondo and yoga can be practiced together. There are both taekwondo courses and yoga courses in the gym, but that kind of taekwondo is not formal. If you are interested in Taekwondo and want to learn it well, you'd better go to a professional Dojo.