If you have tried to resolve the problem with the security company and the property manager without success, all you can do is sue the HOA and the security company in small claims court for the damages you suffered from the tow.
Matters such as this one are annoying, with relatively small amounts of money involved. Small claims court should be the place where this is resolved. Name the HoA and the towing company as defendants. Good luck.
You have not mentioned whether the sign on the parking space identified the association to which that space was allocated. If there was no such ID, you have a good case to file in small claims.
How did the tow company (or whoever authorized the tow) that you were not a resident of THAT association? It would appear that your permit must be different from those of the other association. Otherwise, how wold he know you were not authorized to take that spot.
First I would try a low-key letter to the other association board, stating that your error was caused by their failure to identify thes pace as theirs, and ask for your tow money. If not successful, serve them and contact them again before trial, adding the filing fee and service costs. Still no go? The small claims judge should have no problem giving you your tow charges plus filing fee plus costs to serve the complaint.