Indeed, it does WPS (Lazy, Bridge, and Repeater modes).
I think it would work for your setup...you could interface with it in the car using your phone's hotspot and the remote and then drop the phone out and take advantage of WPS when you're at home to connect to the player.

I'm not sure if WPS would interfere with its client mode while you're driving around using hotspot from the phone, but I think it would work fine