Loading library from name

Does it work if you access it directly instead of using a variable?

One thing that may cause that is when you use $this->library_name, "library_name" I believe should be lower case. You're using $mylibrary, where the variables value isn't lower case.

So it just might need something like:
$this->load->library($mylibrary);
$mylibrary = strtolower($mylibrary); //force to lower case before accessing
$this->$mylibrary->$method();

Did you try it using the actual names instead of variables to test?