Arm and wrist picking

Here’s a new thing I’ve got happening - I seem to be playing with a combination of wrist deviation and a bit of movement from the elbow. I’m trying to go for a pure wrist movement but it often turns into this blend. This for some reason disappears when I play (or attempt to play) metal gallops. One issue I have is that my guitar seems to move, particularly when I tremolo pick, and it’s even happening whilst I strum. Is this normal? Doesn’t seem ideal. Here’s some vids to demonstrate what I’m talking about


Does the shaking make playing uncomfortable? If it does not, why bother? I think it’s unreasonable to think that one should be able to play technically difficult picking stuff whilst holding the guitar perfectly still.