I am a product of the New England Boarding school system. My siblings and I all went, and all boarded for high school. I very much recommend it if possible for your family. The advantages were most obvious to me freshmen year of college, when other students were figuring out how to wake themselves up and get ready for school or trying to motivate themselves to study and do homework, these were things I had already figured out. While some students struggled under the weight of college courses, I was use to the heavy workload. I understand the cost is exorbitant for many people, but if it is something that is reasonable for your family I recommend it. I actually attended two different boarding schools, the first had alot more rich kids (they all have rich kids, but this one has more with last names you would know) and legacy students, while the second had more students whose families took out a second mortgage in hopes of getting their kids recruited. The second one was a better fit for me.
My parents shared custody, so for us, boarding made the most sense as we would be in the same place during the school week. One bedroom, one place to store books and school materials, it made sense. Some students got homesick but no different than in college. I think the alumni system at many of these schools are better than most colleges. I also think depending on the sport and where your daughter would be interested in going to college, it will help with recruitment.
If you are looking at schools in New England and want to PM me a list, I may know the schools or even some people in admissions.