First, if there's just a single schedule shared by everyone, we don't use the plural schedules.
Second, if the schedule or schedules are shared by everyone, it's unusual to use the phrase one anoother's. That's usually used to indicate that things are being exchanged or distinguished between members of the group. For common ownership, we usually use our.
The tricky case is distinguishing between each person having a single (non-shared) schedule and each person having multiple schedules. In both cases, there is more than one schedule involved, so we use the plural word. If you need to resolve the ambiguity, you'll need to express it differently.
So we have:
- Each person has a single schedule each other's schedules
- Each person has multiple schedules each other's schedules
- We all share a single schedule our schedule
- We all share multiple schedules our schedules
There's still ambiguity in the last case, though. It just indicates that there are multiple people and multiple schedules, but doesn't actually say how they relate to each other.