Connecting to iCloud and iTunes: Unknown Error message

Since getting upgrade to ATT internet with fiber, which came with new router, we cannot sign into our iCloud or iTunes accounts through our home wifi. When we try, both come back with an 'unknown error' message.  If we take devices outside on other networks it connects to ICloud and iTunes no problem - cannot with Apple TV and iMac obviously, but we have worked with Apple extensively -  they see nothing wrong with our equipment - they say it's the router / router firewall as we can connect on other networks. I agree, but ATT service could not fix it after additional/different routers being tried.  Didn't close out - just left as is with no follow up as they said the Uverse TV and wifi is working.

I have interrogated the router settings (as far as I feel comfortable) and tried to change a few things but I don't know too much about this stuff, so no success.

Service work fine on UVerse TV, and with searching internet, downloading, Netflix etc, but this issue will eventually lead to losses as we cannot connect with iCloud and ITunes.

Any advice before I start moving my service to another supplier greatly appreciated, as other than this we are happy, but this is a deal breaker.