I am new to Linux too, I briefly used Ubuntu for a year before I replaced my laptop with a smartphone a over a decade ago, but haven't touched it since until 2020, when I bought a Pinephone and installed Debian on it, followed shortly afterwards by my wife buying an ancient secondhand Dell desktop for our then 8 and 12 year old daughters' schooling from home.
Now this PC wouldn't even boot up it's Windows XP operating system and even if it did, the Microsoft Teams software the school used wasn't compatible with it. I fought on a little and got it booting up, only to find myself in a Windows absent driver nightmare, still it was a little nostalgic.
Soon afterwards I installed Debian and it just worked, bliss! During bootups it'd mention two failing hard drive sectors (which has since grown to five over the last several months), but it has worked brilliantly, there is even a .deb Teams package for download from Microsoft's website. I assume it'd work on Ubuntu too.
So far I've just been using StephenBlack's hosts file, specifically the unified hosts plus social networks, pornography and gambling, I can't remember if I just copied it over /etc/hosts with KDE's Krusader file manager, or copied and pasted the text from the downloaded file into the existing file using KDE's Kate text editor, either way it made the computer quite safe for the children. Another possibility is the administrator addon for Nautilus (Gnome Files).
I've read Apparmor might be useful for restricting applications by user, although it has no GUI yet and it's purpose is securing the OS from applications to protect against things like unpatched vulnerabilities, so it'll be interesting to see what happens there.
Last but not least, my answer. Squidguard, check the squidguard documentation on imposing time constraints. I think it can do everything you want, if not a combination of Squidguard and using your hosts file as mentioned above should work. I only discovered it myself a moment ago after not seeing an answer I liked in the replies yet. Another advantage of this is if you use the computer as an internet access point and router (as I do my Pinephone), you should be able to use iptables to transparently route the connection through the squid proxy (I'm assuming that's what it's using) to protect every connected device too.
Edit: Don't forget to backup, you'll be annoyed to lose your configuration and your children their schoolwork and game data. I use Deja Dup to a network drive and Timeshift to a second hard drive at the moment. If you're using Wayland, KDE's Muon Package Manager works almost as well as the great Synaptic Package Manager on X display servers.