Unsure if this will work, but might be worth a shot.
Load the ipvfoo extension into Chrome.
Login to app.plex.tv.
ipvfoo will show you the hosts contacted by Plex Web, some of which seem to be tied to the streaming services - vod.provider.plex.tv, webshows.provider.plex.tv, etc.
You can try blocking the applicable hosts for your kids’ devices during the desired time period.
