OK - Hopefully I now have this resolved. I spent some time looking more closely at Avast One as I had been thinking of installing Avast on my Pixel phone and Samsung tablet. I had looked at other products but I have used Avast for maybe 20 years (?) at least and have no complaints. I had an email offer for Avast One at 50% off for the first year so I called Avast Sales and they walked me through purchasing that, uninstalling Avast Security and installing Avast One. Then they extended my new Avast One subscription for a month to match the old Security subscription. Finally, she deactivated the Premium Security account that was giving me headaches. So all seems good now. Avast One is even playing well with Malwarebytes as have all the other Avast programs over the years. Happy for that as I do like Malwarebytes also. I think I will take a break from this new computer stuff for Christmas!
Then after that I will install Avast One on my phone and tablet and see how I like that.
Thanks again for all the attempts to get to the bottom of this issue. Never really got sorted out, but now it does not matter.