I used to do this with my wife, and it drove me crazy. Now we use a shared Google calendar, which works way better than prior solutions. Our unspoken rule: if there is an open time slot available, the first to enter it in the shared calendar wins. We're both responsible for entering all family-related appointments in the calendar as soon as they come up. There have been conflicts when either of us forgets to enter something into the calendar, but we just resolve the conflicts as usual. This was a game-changer from my point of view.