Perhaps the asylum IS Wonderland in the real (Storeybrook) world. I know it has been said the nurse and the janitor at the asylum are like characters from the movie One Flew Over the Cuckoo Nest, but that could just be their Storeybrook counterparts.
In Alice’s wonderland they could be the Red Queen and her husband!
And except for her hair color, Belle in her blue dress could be “Alice”. Perhaps on her way back to her village (or maybe she decided to return to Rumple), the Evil Queen could have captured her by having her fall into a rabbit hole and end up in Wonderland.
Then when the Big Curse came, all of Wonderland turned into the basement of the hospital. Belle/Alice would logically end up committed to the asylum whether she claims she was the beauty who fell in love with a beast or she was a girl trapped in Wonderland.