Liphook firemen took nearly three-quarters of an hour to cut the family from the wreckage of their black Citroën car. They were taken to the Royal Surrey County Hospital,Guildford.
The mother and her son suffered head, arm and leg injuries. Her daughter suffered wrist injuries and shock.
The twins are pupils at Bohunt, Liphook.
The accident happened on Haslemere Road, near Chiltley Manor around 3-55 pm.
The 62-year-old Liphook woman, who was driving a silver Mercedes, suffered cuts to the head and shock, but declined hospital treatment.
Liphook became gridlocked as police set up diversions. The road was still closed at 7 pm, and there were three-mile tailbacks.
Witnesses should contact WPc Leanna Warwick at Whitehill on 0845 045 45 45.