We've been playing Co Op on 2 Xbox 360s on the same network, in 3 different homes, for years. We have owned several different modem/router combos over the years. Sometimes Xbox were both on Wifi, sometimes one on WiFi and one on Ethernet. I had the old white 360 and my wife had the newer black 360. All this time our Co Op has been fine. We played a ton of games with two consoles on the same network and never had a problem. All the Gears Of War. All the Borderlands. Some DeadSpace. No issues.  
This April we got new Xbox One S systems and 2 copies of GOW4. From about April 6th to April 10 or 11th we played every day in a Co Op campaign on GOW4 and had no problems. Then we had to take break. In that time the only thing that has changed about our set up is that the modem moved about 5 feet and our systems moved. They are still on the same floor as each other. One is in a bedroom. The systems and modem are all no more than 30 feet from each other. One has a wired connection and the other is WiFi. Everything is still connected the same way. Both systems report good connection and all good on the multiplayer when we check network settings. 
During that break our internet went down and my ISP informed me that it had to run an update on our modem. That's the only thing I can think of that changed in any meaningful way. Not saying it caused the problem. But it makes me wonder. 
Now whenever we try to play campaign co op in GOW4 the person trying to join the game gets the following... "ERROR . You have been returned to the main menu. Connection to the game timed out, please try again later". This happens on either system. 
I'm seeing complaints about this going back to Nov 2016. People on PC and Consoles are complaining.  
Currently we can play Borderlands 2 just fine. So is it a GOW4 only issue?  
I'm seeing a lot of info stating that 2 systems can't play on the same network. Both XBOX and Playstation. Since when did this become a problem?  
And what is the fix, other than paying for 2 internet packages?  
Yesterday I was on the phone with Xbox support and we reloaded the games, which took forever by the way -but that's another issue, we removed and downloaded our user accounts, cleared the alternate mac address, cleared persistent memory on the blue ray disk and eventually just reset both Xbox to factory defaults. Nothing worked. 
We use the ARRIS SBG6782-AC cable modem/router. The folks at ARRIS told me that you can't have 2 systems on the same network and maintain an open NAT on both systems. I as able to get an open NAT on one, but when the other Xbox One was booted up it showed a moderate NAT and the previous one either changed to moderate or unavailable. Again, this is all news to me. I never really payed much attention to what my NAT status was. To be honest I'm only just remembering that I've had a NAT status all this time. As I've said.... this has never been a problem so I never went looking for an answer. The only reason I go into my modems control panel is to change our login info for the control panel and our WiFi networks name and password. But now I know I'm reminded of NAT. And it may or may not be the problem according to ARRIS.  
When I told ARRIS that what they were telling me doesn't work had been working they just chalked it up to luck and could not offer real answers. 
I know about port forwarding and port triggering and may take a run at that sort of jiggering to solve this problem. But I'd really rather not. 
Has anyone had and fixed this problem on GOW4 using 2 Xbox One's on the same network and fixed it with port forwarding or port triggering? 
Time Werner Cable... or "SPECTRUM" rather, says that the only thing that was changed on my modem was the radio channel being used by the wireless. I don't know if I buy that, but what can I do? I still think that the modem update that they pushed down the wire actually caused all this. And there is no way to get my modem back to where it was before that update as every time the modem connects to the ISP the update is applied again. So I'm sort of at a stand still there. 
Anyway... Thoughts? Help?