Earlier quoted context omitted.
and 11 year olds grab the computer when you're not there and use it, actually from the age of 8 I think. But yes, browser profiles and computer multi account support are tools that would solve this problem if they worked for the particular problem description - which fair to say they weren't really designed for that scenario so no reason to expect they would work.
You can have your child use the default profile, and have a shortcut whose target is `firefox -P --no-remote` somewhere out of her way. This way, she can just open the browser and use it (on the default profile), and you can click this shortcut to open your profile easily. Just an option to keep in mind in case you decide to get rid of Chrome in the future.
It's really a parenting issue, I could stop her doing it but I don't care enough to do so, and if I don't stop her via parenting there will always be ways she slips through the profile guards.