Blocking Wi-Fi/ internet won't stop apps from launching. The app will likely also cache content that can be viewed even if Wi-Fi/ internet is blocked. The big question here is: Do you get any new content if you try to refresh the app?
What about GSM / LTE / 4G: Maybe your kids phones fallback to that when Wi-Fi stops working?
Suggesting a different solution here: Controlling the devices themselves. With something like "Microsoft Family Safety", https://www.microsoft.com/en-us/microsoft-365/family-safety.