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I had this same difficulty and finally figured out I was doing two things that both contribute to it. One, my thumb was badly placed, and I needed to get it in between the frets I was trying to play . . . so if I was trying to get from 1 to 3, my thumb needed to be right about behind the second fret. (Still does. 😉) The other thing I was doing is keeping my index finger planted, forcing my wrist to do all the compensating.
To retrain myself, I’d just press fret one with the index, then fret three with the ring, and repeat, while finding the best thumb placement for my particular hand and instrument. After a while I found my whole hand/wrist/arm/shoulder complex got more relaxed and stable, and hopefully your case is as simple to fix. 🙂