"I don't know of any young adults for whom clinginess was a lasting problem. They do grow into independence in their own time. It may be much later than average, but that doesn't have to matter."
Saracen, I absolutely agree. Why do people think you have to force everything? DD2 can still be clingy at times and she's 12. But she's nothing like the clingy child she was at 4. She wasn't ready for school either, had screamed her way through nursery until we gave up. "Coped" in school but was never happy. Is growing in independence all the time since she came out of school and felt secure for once in her life. I have very faith that she will go out into the big wide world as an adult and be absolutely 100% fine.
I would never have sent her to school if I could go back. It was, at best, not the right thing for her and, at worst, positively cruel. Like Julie's children, she was very damaged by it. For months all this stuff just kept coming out about how this had happened and that had happened. For the first few months out of school she would say "this is the happiest day of my life", every day. She no longer says it - being happy has become normal to her. What a shame it wasn't before.
In your situation, OP, I'd keep her at home. Maybe, in time, she'll feel ready and want to go. Maybe she'll thrive at home and never want to go. Either way, it would seem better to keep her at home until you reach a point (if you do) that there would seem benefit in going.