Of course there's absolutely no connection between διαμερίζειν and διαμηρίζειν, since the one is derived from μέρος "share," "part," and the other from μηρός "thigh."
That being said, the latter verb would have been written ΔΙΑΜΕΡΙΖΕΙΝ in graffiti using the old Attic alphabet, since eta was not introduced into that alphabet until the reforms under the archonship of Euclides (last years of 5th cent. B.C.E.). So the two could conceivably have been confused in the fifth century and earlier.