I. Your relationship TO someone is usually summed up in a few words and often involves a title. eg "I am her brother", "we are classmates", "she is my ex girl friend".
II. Relationship WITH someone can refer to one of two things; 1. the quality of a relationship with anyone. eg how is your relationship with your father? 2. Romantic involvement. eg "I just met our newest employee, is is true that you used to have a relationship with her?".