You are trying too hard to treat the ice as though it is dry land, I think.

[Not that she's really an expert in this herself, by any means, but this much of the art form, she has managed to pin down.]

It's not. You have to accept it as its own thing, and treat it as such. The movement is different. The way it moves with you is different. To slip on the ground is an unexpected event, yes? But here it's not just to be expected; it's a part of the experience. So, you must not fight to stand still; you have to learn to accept how the ice moves you, instead.