Remembering that the Percy Jackson saga does not follow Greek Mythology in an official way, many of the characters are created or adapted.
Zeus left the Grace family (as is the custom of the gods) and Baryl Grace became unstable. When Thalia was about seven years old, Zeus returned in his Roman aspect, Jupiter. Thalia noted that Zeus in his Roman form was more fatherly and strict with her and spoke Latin frequently. Within a year, Jason Grace, a Roman demigod son of Jupiter, was born.
Jupiter felt obligated to keep showing up at Beryl Grace's house to please her, but he left a second time because she insisted that Jupiter grant him eternal beauty or a visit to Olympus. When Thalia was nine and Jason was two, her mother took them on a picnic, but when Thalia went to the car with the picnic basket, Hera took Jason to Lupa, the trainer wolf of the Roman demigods.
Thalia was heartbroken by her brother's "death" and called his disappearance "the last straw" for her mother and ran away from home, never to return.