In my experience, it depends on the cat. This sort of situation can be very difficult for an animal, especially after spending so much time as an only cat. Is your family still giving her the same amount of affection that she was getting before the kitten came? Its very easy to be distracted by the needy adorable-ness of a baby animal, and unintentionally ignore your long time tennant. It may help if your resident cat sees you and the fam play with and shower affection on her, while occasionally ignoring the baby cat.
Unfortunately, some cats simply do not like sharing their territory with other cats, and see interlopers as a threat. I had a cat who was the sweetest cat in the world to humans. When I moved back in with my mother, she lost her mind over my mom's cat. Nothing she'd done before had given me any inkling that she would behave that way. She wasn't event the resident cat! And unfortunately, it never got better. I had to move into my grandparents' airstream with Daria to solve the problem (which I really enjoyed so it worked out for me ).