Since Then: Carole didn't know about Aaron for the first years of his life. Though she may have learned of Claire's pregnancy, she thought her daughter died in the crash of Oceanic 815. She briefly saw Aaron at Christian's funeral, thinking him Kate's son. Years later, Kate approached her and told the truth. Carole took care of her grandson until Kate and Claire returned for him.
Since Then: The fling produced a child, and Christian repeatedly visited Australia to visit her. Eventually, Carole stopped allowing these visits. When Carole got into a car accident, Christian paid the medical bills. She also tried to get their daughter to turn off the life support. Carole recovered though, and years later ended up attending Christian's funeral.
Since Then: The two had a poor relationship. Claire at one point screamed that she hated Carole and wished she weren't her mother. The screaming made Claire crash the car she was driving, sending Carole into a coma. Doctors said she would never recover, but Claire didn't give up hope and regularly visited her mother. The two presumably reunited once Claire escaped the island years later.
