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she likes her current school because of her friends and she likes the private school because she actually learns stuff... I'm really torn as to what is the best answer here.
No answers, but a few questions -
Have you asked your DD who at the new school seemed like they might become new friends?
Have you thought ahead and discussed how children often change as they grow up... at age 11 or so many outgrow friendships and seek new friends.
Have you discussed that being bored in school may take a toll on her current friendships?
Does your DD see her current friends outside of school... sport teams, dance class, scouting groups, church/synagogue/temple activities, etc... which would naturally afford the opportunity to stay in touch?