Workouts for people with vestibular issues?

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My mum has a lot of issues with anxiety, and I've been trying to convince her to exercise. The main objection against that is that she has vestibular problems, so when she turns her head too fast she gets dizzy to the point where she feels like falling. This happened when she tried pilates at a health center, and now she's scared it will happen again.

Does anyone know of any routines that could take a bit of her stress away while not aggravating her health problem?

Thank you for your time!