Maddalena becomes pregnant with Cosimo's child AFTER his return from exile. However, his son by Maddalena, Carlo, was born no later than 1430, BEFORE he ever went into exile.
Cosimo's brother Lorenzo was NOT murdered. He moved to Rome in 1435 to oversee the Rome branch of the Medici bank and died in 1440 at the age of 45. His namesake, Lorenzo the Magnificent, son of Piero, died at the age of 42 from complications of gout.