If two users are using the Day Pilot scheduler, is there a way to update the schedule for user 2 if user 1 makes a change?
Yes, but it requires some work.
1. First, you need to keep track of individual changes on the server side, and store them as a sequence. Each change would be something like add/remove/update action with the new state stored (and perhaps the old one as well). You can get some inspiration in the following tutorial which implements undo/redo:
You'd have to do something similar on the server side.
2. Then you need a notification service that will deliver the changes to all connected clients. Ideally, it would be a WebSocket connection to the server which will receive all changes performed by the other clients.
3. As soon as you receive a notification about a change, you need to replay the change on the client.