How to establish relationship a Contact has to each Case

I'm developing a case tracking system for social services.  I am using the Contact entity to represent our customers and the Case entity for each social service case they have.

When creating a Case from a Contact form, the Contact is the "Primary Contact."  This seems to happen by default.  From the Case form I need to be able to create and associate additional Contacts representing other people living in the household.   For each Contact they need a "relationship" to the Case.  For example, new contact Sally is the daughter on this case.  But as a Contact, she also may be the mother on another Case.

1. A Case can have many Contacts.
2. A Contact can be associated with many Cases.  This association has a unique Relationship in the context of each Case.

I have created a many-to-many relationship between Contact and Case, but I'm stumped on how to track that unique relationship the Contact has to each Case.

Thanks!