Unfortunately, I am not sure whether I understood your request correctly. You have a Pi that is set up as an access point and connected to the Internet via LAN. The same Pi is also running a Squeezebox Server and Squeezelite and is controllable via Jivelite on a Touchscreen. While it is possible for you to connect another player to the Squeezebox Server via the access point and play music, it is not possible to select the player in Jivelite and play music via an output of the Pi (so to speak „locally“). Is that correct?
For better support please tell me what you want to do with your setup and what you need the access point for.