Anonymous wrote:OP. Should have added: obviously alternating days is fairest. But idiosyncratic professional and caretaking obligations make that impracticable by all accounts, so this question is about how to break a tie, so to speak.
My husband and I have very busy schedules and when our children were small I needed somebody to always watch them, one way we were able to exercise during that time of our life was because we found a fitness center that had a daycare. Prior to that, I took walks very early in the morning or after the kids went to bed. My husband was very overweight it was more important that he went to the gym.