I believe this isn't supported on Fetch, other customers have asked this question on this thread, some provided alternative solutions.
I'll give it a try at home also as I have youngsters and am interested in this too.
Having a look myself it only appears to have Settings > Restriction Mode On/Off
Doesn't look to be anything specific to watching You Tube on your TV based on their support page. Hopefully you can find some helpful information on there. Otherwise controlling access is only available if you live in the European Union