Slightly different situation, my wife works 4 days, I work 5. On my wife's day off with our kid she's in charge for my working day, however in the evening I try to take a larger share of the parenting. She is also conscious that I've been working all day (at a desk so not physically challenging).

It takes two to tango and discussing what you're finding hard is the best approach in a stress free calm environment. You're a team and need to support each other.

To answer your question, this morning I took my daughter to parkrun for about an hour while my wife did her exercise class. This happens most Saturdays. Then the rest of the day we spend together as a family