This topic is of high interest to myself and others. Definitely join our parents group on Telegram (also Matrix).
Currently, we have "Simple Dash" (Brian Douglass) app running over top of regular Ubuntu Touch. This stops any action without parent's password. It works very well, but it does have a back door. You can go around via the settings in the top drawer.
This with Jade Diamond they can only go to a website you authorize. You can also blacklist a website you don't want them to go to.
We are also discussing how the router can work for protecting the whole home in general before the traffic even comes into the device.
Further, we have discussed the topic above of logging in. We believe once Unity8 is working (apparently soon) we will be able to set up 'admin accounts' over top of 'child accounts'.
There are also many business reasons to have these features. Employees should not do illegal or dumb things on company phones.
It would be most excellent to build a thriving team to focus on these solutions. Definitely our kids are getting messed up at young age and we have a very good solution here.
Hope these comments help and inspire....