So you have been doing such hitting, pushing, etc., of villagers since getting your permit? I have read theories about what gets villagers to move. A popular belief is that by not talking to them at all (including not introducing on their move-in day), they move out because the game determines they are 'unwanted,' but if you talk to them you have to build up friendship until they reach a point where they will begin pinging to move.
Hitting villagers seems to complicate things. A common belief is that 'abuse' hastens them deciding to move out, provided you have talked to them at least once (since, if I correctly recall, hitting villagers you have not introduced to will not cause them to get mad).
(Have to submit another VM, as the full message is too long).