My Grandmother who is scottish has always told me that the name Aplin was a "shortend" version of McAlpin.As I'm sure you are aware, the scotch were not exactly welcome in this country at one point and to remove the obvious ethnic indicator of the "Mc" and transpose the L and the P.
I don't know many other Aplins other than my immediate family (We live in Ohio and Indiana.) I am an attorney and know that there is a Criminal Law professor at the University of Cincinnati who is named Kenneth Aplin. Curiously, there is also a department store chain in Cincinnati called McAlpin's.
I hope that this is helpful.I would appreciate hearing alternate theories concering the name if others have them. . .