I have trouble too!
Have had trouble, since the first creatures crawled out of the sea onto the ice.
I think spinning is black art, that can only be done well by those who practice witchcraft!
One thing that helps me a very little is to actually DO things in slow motion. I.E., start from a slow glide, use "stabilizing muscles" to make my body stiff, and make all my motions slow and carefully controlled.
I don't try to spin or move fast, because that makes me lose control and travel. I spin as slowly as I smoothly can.
Since I don't practice witchcraft, I have recently tried putting on a slippery (synthetic material) sock. On my smooth kitchen floor, I stand on one leg, and and very gradually and very, very slowly bring it, and the corresponding arm, around and in front of me. As the arm and leg slow down, I spin spin very, very slowly on the floor. I spin as slowly as I can without jerking. I try to keep my spine erect as I do so.
I bought a full length mirror ($5 at Walmart), and tried facing it as I spin. I can see if I bend my spine at the waist, or anywhere else, or if I lean in any direction, or if my neck tilts - none of which I want to happen.
The problem is, watching the mirror makes me spot (rotate the neck to continue looking in one direction) as I spin, which is not the way figure skaters are usually supposed to spin. (If I were a ballerina spotting would be good.)
I don't know whether these exercises will help in the end, but at least they help make me aware of my posture.
If you have a spinner that rotates very smoothly, you can try it on that too.
I also tried it on a balance board (a flat surface with a half sphere on the bottom). Alas, I can't hold that position without falling off.
BTW - make sure you have space around you for any of these exercises, so you don't bump your head into anything, like a kitchen counter, if you fall - which you may well do, at first. And if you are worried, wear soft padded clothing, or other padding. Maybe even a helmet.
OTOH - if someone else answers you here, take their advice instead. I still haven't mastered this black art.