We have been struggling with this for both girls, so I figured I'd write a post about what worked for us. AM in particular has been having major issues, and her teacher has been on her case to fix it before she can move on.
I have discovered that for us, the problem has stemmed from the fact that AM has been using her hand to actually hold up the violin instead of her chin, so as a result, she was actually using the thumb for support. So once I figure that out, we did a few exercises every day to work on the proper hold.
Exercise 1: Thumb taps.
The idea is to put a finger down on E/A string, and then tap with the thumb on the neck 10/20/40 times. This is hard to do if you use the thumb to hold a violin up.
Exercise 2: No thumb playing.
This was harder to do, but more effective. We did this with scales. The idea is to remove the thumb from the neck of the violin completely and hold it about an inch away, then proceed to play the scale/twinkle. AM needed some help with this, I helped her hold the scroll up, but mostly she managed :)