You may have already integrated your Youtube account with your Vidyard parent group, but when you go into a sub-group within your Vidyard account you do not see the Push to YouTube button.
This is expected. The YouTube integration does not inherit from your parent group down to sub-groups as we do not want to limit your account in Vidyard to one YouTube account.
You will need to toggle into the sub-group that you wish to connect to YouTube. Next, click on the Integrations page on the Vidyard dashboard (Group > Integrations) and connect your YouTube account to that sub-group.