The mother was declared dead at the scene near Barnstaple, in North Devon, on Monday morning.
Her daughter was pronounced dead on arrival at hospital. The girl's twin brother was taken to hospital by air ambulance, but died shortly after arrival.
The family, from Milton Keynes, Buckinghamshire, were travelling on the A361 in North Devon in two vehicles.
The mother and children were travelling in a separate vehicle to her husband, the twins' stepfather, and her 14-year-old son.
Police said the other family members were not directly involved in the incident and are understood to have witnessed the crash.
The road was closed for nine hours while collision investigators examined the scene. The cause of the crash is still under investigation and police have appealed for witnesses.
Inspector Richard McLellan said: "It would seem that a car travelling towards Barnstaple, for unknown reasons at the moment, has crossed the centre white line and hit an oncoming truck.
"Unfortunately the family were travelling in two separate cars but travelling together along this road so dad was there at the scene as well."
Meanwhile, a nine-year-old girl has died after a crash on the same stretch of road a day earlier.
The youngster was travelling in a Vauxhall Vectra on the A361 towards Barnstaple, Devon, on Sunday with her mother and seven-year-old sibling.
They were involved in a crash with a Ford Ranger 4x4 carrying a trailer heading in the opposite direction. All three members of the family suffered serious injuries.
Police confirmed on Wednesday that the nine-year-old girl died in hospital on Tuesday morning.
The incident happened near West Buckland at around 11.30am. The driver of the Ford suffered minor injuries and was released from hospital.
Police have now launched an appeal for witnesses. THINK YOUR FRIEND WOULD BE INTRESTED? SHARE THIS STORY USING ANY OF THE SHARE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>