You need what we call a "many-to-many" relationship structure using a "join" table.
Organizations (table)
Contacts (table)
Organization Contacts (table)
Organizations < Organization Contacts (parent < child)
Contacts < Organization Contacts (parent < child)
You probably have yours setup as Organizations < Contacts; but you need to separate the two so they act independently and then create the "join" table between them that allows you to associate one contact to one or more Organizations. Then you will be able to see in the Contacts table which Organizations that contact has been associated with.
