What does a screen-free Sunday look like when one parent is usually working?

Every 'screen-free weekend' plan I've read assumes two rested adults, a park nearby and a craft box. In our house one of us has a clinic shift or a client review most Sundays, the younger one is up at 6, and the older one will negotiate anything. We tried it last Sunday. It lasted until about 11, when I needed thirty minutes to cook and the TV went on. If you do keep a screen-free day, I'm interested in the ordinary version: who does what, at what time, and what fills the hour before lunch when everyone is tired?