There is not a "closed style" and an "open style". A woman, unlike a man, has hips wider than their shoulders. Therefore, the hips have to open to let the arm go by or the arm will hit the hips. All accomplished women pitchers open the hips, let the arm go by, and then close the hips. However, the amount the hips open and how long the hips stay open varies from pitcher to pitcher. In other words, all pitchers get open, some pitchers are just "more" open than others.
The reason a more open style is preferred is because (1) it keeps the legs and arm in a neat line, allowing a more efficient power transfer, (2) the arm can go in a nice circle without changing planes and (3) the pitcher doesn't have to worry about hitting the hips with her arm.
Whitney Canion is the poster child for "getting the hips open" and leaving them open.
Here is Dallas Escobedo of Arizona State. It is clear she opens the hips, lets the arm go by, and then closes the hips. She closes earlier than other pitchers, but is slightly open when the arm goes by the hips.
Most instructors would say Canion has better form than Escobedo. But, Escobedo has been very successful. IMHO, Canion is slightly better than Escobedo, but obviously both are very, very good.
The vast majority of successful college pitchers pitch more like Canion than Escobedo. Go to the "Model Pitchers" thread, and you will see lots of different pitchers. All of them, other than Escobedo, open and stay open. Even Uneo stays open longer than Escobedo. So, if your DD is going to play the percentages, you would go with a more open style like Canion.
I have seen many, many pitchers with a form similar to Escobedo, and they have all failed miserably. I think Escobedo makes it work because she is enormously talented. It would be foolish to assume that anyone's DD is as gifted as Escobedo.
Perhaps you have heard of Stan Musial. Musial is one of the greatest hitters ever. No one teaches his method of hitting, because only a person with incredible talent can hit that way. People like Escobedo and Musial come around only once or twice a decade. Don't bet your child is one of them.