Seeing family members on Case Form

What I'm trying to accomplish gives me a brain cramp, so am reaching out to the community for help.

1. I use the Case entity for social service cases. 
2. I use the Contact entity for the social service customer.   Creating a Case from the "Related Cases" subgrid view within the Contact creates the "Customer" relationship (magic I did not create).  That Contact ends up being the "primary" contact.
3. Each Contact has a potential familial relationship with others.

I want to show the "family members" view on the Case form.   This is basically the Connection between the "Primary" contact (customer) and other contacts.

I'm so confused with sub-grid versus QUick View as well.