This is strictly a matter of personal comfort and preference. It's possible to use bad technique with any chinrest, and it's possible to use good technique with any chinrest, but some will feel better or work better for each person. The violin was played for centuries with no chinrest at all! I decided on a chinrest model that I liked in my teens, but later changed the way I hold the violin slightly and then used a different chinrest. (I currently use the Guarneri, the top left corner in the picture of chinrests; it's a very popular choice.) The best way to choose a chinrest is to go to a store that has many models and try them on. If your daughter is just beginning, she might find that one is more comfortable than another, but as she learns more technique, that choice might change later.
The chinrest your daughter currently uses doesn't cause bad left-hand technique, but a different one could help it. Your teacher understands best what they meant by "butterfly, not crane." These kind of metaphors are great for helping students remember physical positions (I use "parrot, not fox" for right hand), but I'm not sure what it actually meant for the hand position. What is true is that the hand position can be affected by where the violin is placed on the neck and the direction that the violin points, and these can be affected by the chinrest and shoulder rest models and how they're positioned.
The shoulder rest is the "support under the violin" that Tim mentioned. Teachers have different opinions; for very young children (like 5 years old or less), some prefer not to use them. Some players start with them but later decide not to. Personally, I recommend them for all beginners. For this, too, you will want to try different models after learning for a while. Experimenting with where the shoulder rest is placed on the body of the violin can be useful too.