You should have relations in the database.
As the other answer notes, performance isn't a considerationof constraint checking will be far better inside that database than inside your application. Database constraint checks are one of the things that databases are very good at.
If you ever need additional flexibility - e.g. your noted cross database references - then you can remove the constraints deliberately and with consideration. Having consistency within your database means that you have the option of modifying those constraints, and certainty of referential integrity.