It doesn't do full mirroring with the app? Can you explain what you mean by small version? Do you mean it just shows vertical and black on the sides?
What phone are you using?
Could just be auto-rotate or orientation lock is on.
Worst case if it's the limitation of the app...
You can add a Chromecast. I added one to my factory head unit. Had to us a HDMI to RCA converter. Plugged the Chromecast into that. Then launched it AV-IN.
To get it up and running, I set it up connected to the home WiFi. Then ran it off the phone's hotspot and tricked it into running off itself. Complicated but a working option.