*On checking the history of websites I then find I have supposedly visited at least 3 sites on a day there was no one in our home*
Do you mean the history stored in the browser?
Do you go out and leave your system powered up and connected to the web?
The history stored by the browser of visited sites cab only be if your actual system has visited those sites. If you are totally sure that there was no-one who could possibly have used your system unknown to you on those days and times - then only some fairly clever hacking could have done this. I would suspect a more mundane explanation.
Is the CC fraud connected with your unexplained web-site visits?