Sounds like a network latency issue to me, the clue would be that the users connected to the onsite server have no issues. I would try moving a user with the problem from the remote server to the local server and then seeing if you get the same issue.
I have one public folder calendar setup and 2 users added as owners.
User 1 can create appointments and user 2 can see them. User 2 can't create appointments so no one can see them!
Both users are owners.
Why is this not working for user 2?