Juliet and her mother have a typical aristocratic/royalty relationship. The children are closer to the nanny/governess than they are to their parents. Juliet has a formal relationship with her mother based on duty and respect, but not emotion.
Juliet shares a more intimate relationship with the Nurse. It is the Nurse that she talks to and confides in and seeks out for comfort. Juliet does not have a close relationship with her mother, as is usually the case in aristocratic or royal families when the children are raised by Nannies and Governesses. The children naturally bond with their caretakers who are around all the time.
Think of Prince Charles of Great Britain, he is not close to his mother, for most of his life she was away touring the British Empire as Queen. This was one of the problems that Princess Diana had with her husband. She wanted to be a hands on mother with her sons, William and Harry. And, for the most part, Diana was a very involved, loving mother to the two Princes, very unusual for royal circles.
The relationship could at worst be called cold, but would probably best be called "formal". They are not warm with one another. Their is no trust and comfort between them. Juliet has been, in the custom of the time, raised by her Nurse, who not only breastfed Juliet, but also served as her confidante and comforter. The proof of this is evident when Juliet seeks out the Nurse for assistance in securing Romeo.
However, the scenes between Juliet and Lady Capulet show two people who are mere acquaintances. When Lady Capulet approaches Juliet about the idea of marriage, she is not comfortable to do so without the Nurse present. Juliet's responses to her mother are short and obedient - she calls marriage an "honor" and promises to be ruled by her parents' consent. Later, after Tybalt's death, Lady Capulet comes to Juliet in the belief that she is bringing news that will comfort Juliet. In this scene, as she tells Juliet of the impending marriage to Romeo, Juliet is sarcastic and deceitful in her answers, and much less obedient. Now she is married, she has no use for her mother, and has no sense of loyalty to her. Lady Capulet does not know her daughter enough to realize she is lying.