I don't see the point in even concerning yourself with whether it is a walk pirhoette or a turn on the haunches. It doesn't matter. What you are doing is basically playing with your horse, exploring her body and her willingness to do something new, and working to encourage her 'try' and all that.
I think it's rather cute to see the two of you 'playing' together. people should 'play' more with their horses. I think your mare is listening to you and giving you a really nice try. And, you can help her a little bit more by working with her to have more softness in her poll and jaw.
Her conformation has her with a very straight neck, which will make it hard for her to bend there. However, patient work asking her to flex at the poll, both vertically and more importantly, laterally, will help.
If you really want to get a critique on your riding, or on your horse, don't do it bareback. take away that 'excuse' and ride with your best advantage.