I have reinstalled Windows with reformatting our 'family' computer on a number of occasions. It is never quick or easy but as a last resort often the only thing left to do.
Did I mention System Restore? I believe I did.
To add to my last you should always backup your files. That goes without saying, which is why I didn't say it. Then you have an external drive with all of your files on from which you quickly copy to your newly formatted original hard drive. Quite straightforward really considering what you are doing. Unlike what BOAC and Gertrude are implying. I backup my important stuff onto several external hard drives.
With this being your 'family' computer you either have to do all of this regularly or stop them from going onto dangerous websites. I would say do both as and when necessary. Otherwise don't start a family.
