If you're using a whitelist approach, you may as well just turn off the internet. Maintaining a whitelist is almost hopeless. Turning off the internet isn't a bad idea, but it is a big change. Maybe some form of archiving interesting pages for kids to look at, but even that feels like too much work.

Plus, if you're using the google docs ecosystem, I suspect it's hard to avoid kids chatting in shared text files, and eventually figuring out how to get spreadsheets to fetch webpages for you.