Well it would seem I have just found the source of my troubles. I am hoping this was the only issue and crossing my fingers things have now been rectified. Time will tell.
In a nutshell, the .htaccess files on both my domains had been hacked and injected with malicious code designed at redirecting users arriving from a search engine listing, which sure explains why Google was so motivated in flagging me.
It appears that my web host, IX Web Hosting, is having huge security issues. I’m not surprised, one gets what one pays for. I had hoped to be in better hands then with GoDaddy. It looks like I am not. I might have to switch again, to a safer server this time, hence more expensive.