An asylum is actually a perfect place to start a twisted story of any type.
In a twisted wonderland anything could happen, correct?
Well it could be any form of character (from wonderland) who was sucked into wonderland at an earlier time frame. The hatter could have gone psychotic with something that happened in only his/her dreams. Then the more time that had gone by the dreams became nightmares then slowly ate away at reality causing the hatter to crack completely.
Or maybe the cat drove the queen mad with it's smile and conniving ways. It set her off and things go bad.
Or something could taint wonderland then eat it away.
My character could be anything. Be a main character, a random oc in wonderland, or even an asylum patient. Just depends on how you want the story to grow dark, if it was already dark, or whatever.