Controlling children’s internet activity is nothing new. Parents have been dealing with that (or fighting their kids over it) since people started having home computers.
Unfortunately I am not aware of any consumer-grade (in other words, affordable) routers that do what you ask. I’m not aware of any standard setting that will somehow throttle the internet speed.
But there are alternatives.
Few kid-proof solutions
I have to start out with a fairly big caveat that many parents have a difficult time accepting.
If there are routers that have parental and other kinds of controls that might be able to do something, your kids are probably smarter about this than you think. Or they have friends who are.
Ultimately, whatever you end up putting in place may be easily bypassed. This is is something I hear often. Many parents put technological solutions in place only to have their children just sneak around it somehow.
I have heard of parents doing something a little bit lower tech: they put the power supply for the router on a timer. Just a regular old lamp timer so that the router shuts down at a certain time of night. In the morning, it turns itself back on again.
There’s actually nothing wrong with doing that. It shouldn’t harm the router. It’s just that the internet and probably your local network will be completely gone until the router is turned on again in the morning.
You do have to be aware that you want the router and the timer to be physically secure. In other words, you want those things to be in a location where your children can’t access them. Naturally if all they need to do is unplug the timer and plug in the router again, they’re going to do exactly that.
Ultimately, I don’t have any great solutions for this. I am posting this article so that perhaps some of the readers who have children and face issues like this in their own homes will have some ideas for us.