If your daughter is playing for a top club team she’ll get the exposure she requires to be seen by college coaches whether she goes to private or public school. Going to private school just for the purpose of getting a college scholarship is just as expensive as paying for College itself. And if you are using lacrosse to get into a better college- just focus solely on academics in the first place. Nothing wrong with either private or public as I have a child in each but just be realistic with why you are doing it.