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King, 74, married actress Southwick, 48, in 1997, and the couple have two children together, ages 9 and 8. She also has a 26-year-old son from a previous marriage.
Her father, Karl Engmann, tells PEOPLE: "She's had migraines her whole life, ever since she was a little girl, and she finally decided to do something about it. We're happy she's taking care of herself and everything will be fine."
CNN had no comment.
– Michael Y. Park
