Juliet has a strained relationship with her mother, who loves her but is rather distant. It is the Nurse who has brought Juliet up, having been her wet-nurse and then her Nanny and continues to be employed by the Capulets in this capacity. It is no surprise, then, that Juliet finds the Nurse much more mother-like than her own mother.
Her father is more interested in seeing that she marries well and soon rather than her personal happiness. He tells Paris that although she is "free to choose" her own mate, it must be from a narrow pool that he has approved of, and what's more, he has already selected Paris. He sees no reason why his daughter would object.
In 3.5, Lady Capulet believes Juliet is weeping for Tybault. She is suprised by the reaction and more or less tells her to get over it, she looks stupid. Not exactly a kind response! (Not to mention off-base.)
"Evermore weeping for your cousin's death?
What wilt thou wash him from his grave with tears?
And if thou couldst, thou couldnst not make him live.
Therefore have done: some grief show much of love,
But much of grief shows stills some want of wit." (3.5.70-73)
Her refusal to marry Paris meets with anger, not understanding. She sees no reason why such a match would not "happily make thee a joyful bride," but when Juliet protests, Lady Capulet exasperatedly tells her that she'd better take it up with her father: "Here comes your father now, tell him so yourself / And see how he will take it at your hands" (3.5.124-125).
She doesn't truly side with anyone, but it is clear she is not much on her daughter's side.