There are some good routers out there that successfully manage access. Examples include Draytek and Fritzbox. I use the latter and there is WiFi control, but also WiFi for guests that limits access to the device itself rather than the entire network, therefore preventing any modifications to the setup etc (I use it for a couple of dubious IoT devices like my govee thermometer which i use to monitor my freezer's temperature.) So, you could have two WiFi networks: one for you and the other (guest) for your children. Fritzbox also allows lan port 4 to be used for guests.
There are other measures that you could take which are outlined here: https://en.avm.de/service/knowledge-base/dok/FRITZ-Box-7490/8_Restricting-internet-use-with-parental...
I suppose this wouldn't stop your kids from changing active lan connections (swapping cables), but if you're very determined and want to show your kids that, then you could always lock the router in some kind of enclosure to prevent that. That's going to extremes, obviously, so my advice is also educating your kids about why you'd want to limit access to the internet but also trying to treat them like adults by teaching them to be more responsible for their own learning and managing access. How are you going to stop the kids from using 4g, though?
With Draytek you can go further by setting up a time limited access to the internet. Something similar to airport WiFi access where you need to log in and then you can only access the internet for a specified amount of time, usually an hour. Then you can either apply for more time or would have to wait. Set up possibilities are endless, but I'd encourage you to research before you commit to buying a new router as this kind of equipment can be very dear. Plus, when you're fast asleep, would your kids not swap routers round, without your knowledge? https://www.draytek.co.uk/information/our-technology/hotspot-portal
Both Draytek and Fritzbox also offer to block specific apps or pages (for example Insta), but if you want to go even one step further, you could also use blocking at DNS level to stop your kids from researching stuff on forums.
