Hi,
1. Make sure that the wired Apple TVs are on the Airgroup Servers list, i.e it should have layer 2 connectivity with IAPs.
2. Check if guest user device is on the Airgroup user list.
3. The 10.0.1.x networks should be reachable from 172.16.10.x network, i.e guest user should be able to ping the Apple TV.
4. There should be no NAT between these networks.
With 1 and 2, guest users can discover the Apple TV.
With 3 and 4, mirroring should work.
Thanks,
Rajaguru Vincent