Alright, this is what I see the mare doing....
She isn't using her hind end at all when turning, she isn't following her nose at all (like SH said), and she is REALLY getting on he front end. So I would work on getting her shoulders where you can move them whenever you want. I like counter arcs, side passing, and a lot of moving the shoulders.
She is very bendy which means she isn't moving her shoulder which is making her butt swing. You need to get that shoulder freed up and moving. I have a running mare that occasionally wants to noodle up on me completely and pop her shoulder out while staying engaged every other place. I pack a little whip to tap her shoulder when I feel her on the backside wanting to drift that shoulder out.
You should really work on stopping and backing (getting her to really use her hind end properly and not front end), do some rollbacks and turn her into the fence making her have to move that shoulder over and plant her hind end.
With my mare I like to mess with her head a lot and keep her on her toes, so I will randomly stop ask her to back, or randomly ask her to plant and spin a few circles and keep that shoulder moving and butt planted. When coming to a barrel during slow work I will ask her to stop, and counter arc her then push that him in towards the barrel lift her shoulder and ask her to go around it like that (I really make her over exaggerate it and have gotten weird looks lol).
Here she sorta noodles on me on the backside of 2nd and 3rd but not as bad as she sometimes tries. I love this mare because when she is really paying attention and not lolly gagging around she has a Martha style and can just melt around the barrel and have a beautiful engaged smooth pattern and turns.
Make sense? Been a long day so not sure if my rambling is understandable lol.