Bands around the ankle increase the difficulty of the exercise because it increases torque at the hip. Other than that, it's all about personal preference and which way feels more comfortable for you.
Yeah, that's a good way to look at it! Aside from just bad luck accidents a lot of badminton injuries can be traced back to some sort of misuse or misalignment in your body. I used my tennis elbow to not only to improve my arm while playing but I changed many things in my daily life that were also aggravating it. I'm now dealing with a little jumpers knee pain and trying to improve my thigh muscle to prevent it from getting worse. Important lesson is don't take your ankle for granted anymore. Whatever you are doing to improve it keep it up even after the pain is gone. I feel like badminton makes us much more aware of our joints than other people.
Honestly, that ankle is just weak. The first two times I sprained it were when I played right handed, I switched to left handed, and 18 months later and I sprained it again with completely new footwork etc, not even the same handedness. It wouldn't surprise me given my hypermobility in other areas. I got some resistance bands today, been doing lots of shadow strokes outside in the garden with my new N9, building up speed and strength in my arm til I can play again.
Jumper's Knee could also be due to a weak IT band putting a lot of strain on the knee and not only the thigh muscle. I had a similar issue.
