You've initiated a chargeback. I would not do anything else as that can only gum up the system. The property, if it wishes to pursue the chargeback, will need to document the second reservation for the CC issuer. In the meantime, you presumably have a temporary credit so you aren't paying for the room.

If the chargeback succeeds, you are done. If the chargeback fails, all your other options remain open.

In the meantime, double check your email for the day the second reservation was made (and perhaps 1-2 days after) just to make sure there isn't any odd email regarding the second reservation. Check your email spam filter to be certain.