I'd recommend using an RDS like SQLite. SQLite is an RDS that stores the database in a binary file, and has a SQL command line interface. This recommendation comes from my experience teaching web development (and using an ORM to interface with the database), because I've never had the opportunity to teach a database management course. It has GUIs, such as SQLite Studio (Disclaimer: I've never used this) and is fully cross platform. It also provides a good stepping stone to more typical production databases such as PostgreSQL, MySQL, MS SQL Server, etc.

SQLite is also open source and in the public domain.

Disclaimer: This recommendation comes from my experience teaching web development (and using an ORM to interface with the database), because I've never had the opportunity to teach a database management course.

I'd recommend using an RDS like SQLite. SQLite is an RDS that stores the database in a binary file, and has a SQL command line interface. I find it fairly simple to use, and a good introduction to how relational databases work and how to interact with them. 

It has GUIs, such as SQLite Studio (which I've never used, but looks useful) and is fully cross platform. It also provides a good stepping stone to more typical production databases such as PostgreSQL, MySQL, MS SQL Server, etc.

It is also open source and in the public domain.

If you choose to teach from the command line interface, that'd easily eliminate the GUI related issues you mention in the question, and would also force the students to interact with the database using SQL (which is a good and bad thing).