Simon Lewis, 33, died when Kyle Kennedy, 29, hit his car head-on in a crash in the Tremorfa area of the city on New Year's Eve.
His son was delivered prematurely three days after the crash at University Hospital of Wales but died later the same day.
Kennedy, from Rumney, will be sentenced on Friday at Cardiff Crown Court.
The court previously heard he was driving at "motorway speeds" of up to 70mph when the crash on Lamby Way happened.
He had denied two counts of causing death by dangerous driving but was found guilty by a jury. He had admitted causing death by careless driving.
On Wednesday, Kennedy told the court Mr Lewis was godfather to his cousin's child.
He said he took responsibility for his actions and offered his "deepest sympathy" to the family.
But he told the court the crash would not have happened if a van had not braked in front of him - although he admitted being too close to the vehicle.
Amanda Lewis, Mr Lewis's widow who was pregnant at the time of the crash, said in a statement her husband had shouted and sworn before she saw lights coming towards the car.
The next thing she was aware of was her opening her eyes and hearing herself making a noise and her daughter screaming in the rear of the car.
She said Mr Lewis who had been driving was lying flat on his back and not responding or moving when she told him to wake up.
The court heard she screamed when she was told he had not survived.
Three days later, Amanda Lewis underwent an emergency Caesarean section, but her son did not survive.
A Cardiff driver has been found guilty of causing the deaths of a father and his baby son.