You need one more adapter to connect to the AP.

One given WiFi adapter cannot be connected to an Ad-Hoc and an Infrastructure network at the same time. You need a second WiFi adapter to make the bridging between the networks of two different types, and make sure Daihinia driver is NOT bound to the adapter that connects to the AP. In the event that bridging does not work, the job can be done at the level of IP subnetting and routing.