No a second hard disk will not make a difference.
Your problem I suspect is that the database is Access when you will really consider porting it to something like SQL Server, especially as you are using it across a network.
Your problem is that Access is not really a try multiuser database platform, and it works via a single flat file system. SQL Servers such as Microsoft and MySQL work across various data files each per database table, and are threaded for mutliuser usability.
Put simply, it sounds like you have outgrown your Access database.
For short term solutions I'd look at your network, make sure you are running on at leats 100mb ideally 1000mb and that you are using a network SWITCH and not a network HUB to link your pc's together.
Switches are more intelligent and send traffic to the port/pc that is asking for that data (direct link between ports when a pc talks to the server for example - faster method). A hub will send data to all ports, so when the server sends packet of data to one pc ALL pc's get that data and it is left for the other pc's to dump the information saying "I didn't ask for that" (ie. slower method).