My heart goes out to you... After watching both videos and knowing she only does this sometimes makes me think there is possibly something else going on.... It could be spinal as @2BullyMama pointed out and also @LariP pointed out it does almost seem like she's trying to get an itch. I would check tail pocket, vulva, and under her rear paw pads as well.
I'm curious to know why your vet diagnosed severe hip displaysia but didn't refer you to an orthopedic specialist. Are they considered experts in that field? Most vets are not and always refer to a specialist, that's why I'm wondering.
I hope you get some more answers and soon, this has to be weighing on your heart so heavily!
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