Chrome browser adware / malware? cannot close window

No malware has been installed or downloaded.

That is merely a Javascript in the browser designed to fool people into calling a phone number and give criminals access to your computer so they can steal money.

Force quit chrome.

Restart it by holding shift and clicking the chrome icon.

Clear cookies and browser cache.

Please read Phony "tech support" / "ransomware" popups and web pages for a description of, and the solution to, this common scam. Have your mother read it as well, as well as forward it to anyone else she cares about. Although it is written specifically for Safari, its instructions are easily adapted to other browsers.

We did download and run Avast Free Mac Security...

Use Avast's uninstaller, which will remove it completely. Use no other technique, utility, or procedure. "Avast" is arguably malware in itself. Don't use such things on a Mac.

Should we reset the router?

There is no harm in doing so, but it is not necessary unless the problem is similarly affecting all the devices on that LAN.