A 59-year-old woman killed when a car ploughed into her was with her two grandchildren at the time.
A grey Volvo C70 hit a lamppost and the three pedestrians on the High Street in West Wycombe, High Wycombe, on Wednesday morning.
A nine-year-old boy and five-year-old girl are in a serious but stable condition in hospital.
The 46-year-old female driver has been arrested on suspicion of causing death by dangerous driving.
She has also been arrested on suspicion of driving while over the prescribed limit, and is being questioned, police said.
Two crews from High Wycombe Fire Station and three air ambulances were among the emergency services at the scene.