I want to second what dandelion just said and add that part of the EY experience is exactly why she’s having a hard time – being away from home for an extended period of time, learning to be independent and immersing herself in learning more about Yiddishkeit than she probably learned in 4 years of H.S.
Rebbetzin Shain wrote in All for the Boss that part of the reason that she and her husband, R’ Moshe, were so close was because they had gone to Poland early in their marriage and had to learn to rely on each other. They developed a special closeness that never dissipated over the years, no matter that they returned to the U.S.
Your daughter will learn not only Torah, but all the skills that other people mentioned above, including how to make lifelong friends probably on a deeper level than those she had in school simply from proximity to their house/being in elementary and high school together, and the kedusha of EY will give her koach that she didn’t know she had to rise in ma’alos of yiras shomayim and avodas H’ that will carry her to marriage and beyond.
You all should have a gut gebentsched yahr and H’ should send you parnasa meruba to be able to send your next daughter to EY as well because I have a feeling that after she talks to her older sister a few times once she has adjusted, she will also be begging to go to sem in EY.