I'm looking at this from a middle school perspective. One of my DDs has a summer birthday and is on the young side for her grade. She is accelerated 2 years for math as it is, and will start taking high school classes as a 13 year old 8th grader. The idea that she should be in 7th grade and the school accommodate her -- when she wouldn't even be in her age appropriate grade -- seems silly to me. We are very blessed to be in a flexible school that tries to meet kids needs, but I think parents play a role by putting them in the right grade to start with.
Sure, some kids are better off having a bit more time. I'm not arguing with that. I'm just saying that the OPers DD doesn't sound like one of them.
And it's 3 hours a day. It's not boarding school. She isn't loosing her family.