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As far as I can tell from this angle, your form is good. It may sound awkward now because it's not very fast, but it will sound more natural as you speed it up. (But don't rush into trying to play fast vibrato.)
If you feel like your hand is moving out of place: what is your thumb doing? It's not visible in the video. Whether you're playing arm or wrist vibrato, your thumb should stay at the same point on the neck, but should pivot at the contact point to allow your hand to move.
Wow congratulations!!!! Keep it up like that. With time the motion will be stuck in your muscle memory and gradually you will be able to get it up to speed. Dont feel bad if you feel your pink doesnt quite do the job. It is indeed the weakest finger and it will a bit of more time to get it used to vibrating. Keep doing your scales always focusing on the motion each finger is doing. You are doing great!!!
There's nothing better than a cold beer and the warm soothing sound of a violin.