In a Sonos environment, when a soundbar has surround speakers added, they are “bonded” in the same way as a Sub. This means that a dedicated, one-way 5Ghz wifi link is created from soundbar to rear speakers (or Amp, in your setup). Any line-in capabilities the rear speakers have are disabled because the link is one way: there’s no link back from surrounds to soundbar. Even when Ethernet cables, any rear speaker/Amp inputs are disabled. 
So no need for wires between Arc and Amp; leave them wireless and see how the system performs. 

The sonic results will be the same - wired vs wireless. Since 5GHz does not penetrate walls very well, a wireless surround AMP should be in the same physical room as the soundbar.

If you have dropouts or lag, then try Ethernet between arc and amp

Ethernet between Arc and Amp or via router?

Been told either between them both or to shared switch, or router i guess wont matter…

Thanks all. Got rid of the wired connection between  tv and amp in favor of a wifi connection between arc and amp. This solved the problem of the tv getting confused between arc ultra/amp both being connected and not knowing which to prioritize. Then, I connected the ceiling speakers to the system by adding the amp to the Sonos/sub 4 system by selecting the ‘add surround’ choice in app. That got all the speakers working and talking to each other. Then, used True Play advanced set up and the system balanced the sound with the in ceiling speakers. Final result: balanced Dolby Atmos sound in our space using the arc ultra, sub 4, and in ceiling speakers connected by an amp. Thanks all!