Use a server based database - SQL Server, or MySQL - and that is exactly what it is designed for.
You can either produce two separate applications, one for teacher and one for students, or one app that requires a teacher to log in before accessing the "advanced features".
You would need a computer with the server software installed to host the database, and that PC should be accessible from each PC (it can be on the same LAN segment, or via the internet - though that is harder as you need more layers of security to prevent unauthorised access).
You can download a version of SQL Server from Microsoft for free (the Express edition) for development:
SQL Server Downloads | Microsoft[
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