on my I-mac how do I check the router history on all sites visited?

Check the IP router you’re using? Some IP routers track traffic, and some do not.

A typical IP router generally has no view into the URL, however. IP address and port, maybe DNS if that’s also being logges.

As for macOS and Safari, check ~/Library/Safari/history.db for each user.

Other browsers track history differently.

There are various forensics-related papers available, depending on what you're up to here. Hereks one such paper:

(PDF) MAC OSX Forenscis

While you’re on the phone with AT&T, and if the features and logging of that box are insufficient, ask them if the device can potentially be placed into a “bridged” mode and with the addition of a mid-grade firewall-gateway-router of your choice. That’ll give you better control and logging capabilities than most any ISP box, if you’re inclined to pay for, install, configure and manage that.

on my I-mac how do I check the router history on all sites visited?

What is the make and model number of your router?

"Bridge Mode" is a setting that will never be found on an ATT provided router, but some of them will allow a user to set up a DMZ mode or IP Passthrough mode for one device, which could be another router. More details here:

Configuring IP Passthrough and DMZplus - Internet Support - ATT.comhttps://www.att.com/esupport/article.html#!/smb-internet/KM1188700

Check with ATT support to ask whether or not their router has logs that track Internet connection history. I doubt that it does, but you never know.

If the answer is "yes", ask ATT support how those logs can be accessed.