Django is a pretty powerful framework for web apps. I think your app sounds pretty doable. You'll just need to store some playlist metadata in a db. Probably a schema like this. Django and Keystone both include an admin panel you could use to manage the configured playlists:

url
name
scheduled_datetime
runtime

Then your app logic will pull all playlists out of the DB that are scheduled for a time later than or equal to the current time, and sorts them into a chronological list based on scheduled time. Your app's validation logic would need to ensure that you can't set any scheduled_datetime that collides with an existing playlist.

As for the front end, buttons and players are easy. You just initialize a player with the playlist urls.

https://www.djangoproject.com/