Hi Mary,
The first thing I'd make sure of is that in fact you are both posting to the same data set. On both machines, log into Adagio Ledger and on one machine create a batch. On the other machine, does that batch exist? You might need to check your shortcuts or otherwise verify that both users are pointing to the same database. The database location appears in the status bar at the bottom of the window, and when you move your mouse over top of this, the Company Name appears to the left of this. The most recent Ledger release (last week) also puts the Company name in the window Title.
Once data is posted to a shared location, it will be accessible from any machine that can read the data successfully. It doesn't make sense that data can only be read from only the machine that did the posting. It is possible that something 'goofy' has occurred on the system. Try this: in the above case have one user edit the created GL batch, then have the other user attempt to edit it as well. The second user should get a message that the batch is already in use and cannot be edited. If you don't get that message, then the record locking is set up incorrectly and certainly data corruption is a real risk.
Is you network server dedicated or is it also a workstation (ie peer-peer connection)?
Regards,