General AirPlay and Remote App not working

[Mammut]

I'm facing a strange problem the last weeks and I'm out of own ideas how to fix it. First of all some info about my setup:

1 Apple TV 4 (WiFi) (tvOS 11 & 11.1 Beta 3)
1 Apple TV 4 (cable) (tvOS 11 & 11.1 Beta 3)
1 MacBook Pro 2017 (WiFi) (macOS 10.13)
1 Media Receiver (cable)
1 iPhone 6s (WiFi - obviously) (iOS 11 & 11.1 Beta 3)
1 iPad Pro 10.5 (WiFi - obviously) (iOS 11 & 11.1 Beta 3)

First of all: AirDrop between iPad, iPhone and MacBook is working correctly. The devices find each other and it's possible to share files between them. Also working: AirPlay directly from MacOS. I can duplicate my screen on both Apple TVs.

What's not working:

• Getting access to the media library on my MacBook from both Apple TV devices
• Controlling iTunes or both Apple TV devices with the Remote App from my iPad or iPhone
• ATV Remote App
• AirPlay from iTunes to my Apple TV devices or the AirPlay capable Media Receiver

I've checked all the ports and settings on the router / access point - totally fine, can't see a problem there. I've de- and reactivated private sharing on all devices - without any bettering. I've restarted all the devices (including the router)... nothing. Same for resetting network settings.

Any ideas?