You want to ensure that the ATV and iTunes use the same Apple ID. You have to enable it on both devices.
For AirPlay, Bonjour discovery should work. Is the ATV connected via ethernet or wifi? My guess is wifi, because the iPad/iPhone should connect over wifi and can see the ATV. Is the MBP connected via ethernet or WiFi? If the ATV connects via ethernet to the rest of the network, does the MBP detect the ATV when connected to the same switch/router?.
If you use something made by Netgear, it does network segmentation depending on what you use. You can use a Bonjour browser to see devices on the network. If you want to use something like packet captures, you can try Wireshark.
Do you have a firewall application on the MBP? Look under System Preferences -> Security and Privacy -> Firewall Tab for Apples, or if you have third-party software, look at their UI.