Police officers allegedly smashed a car window as a woman who said she felt “too threatened” to leave sat in the driver’s seat with a baby on her lap.
A complaint has been made to Hertfordshire Police about the episode said to have happened on the A10 in Cheshunt.
The woman, her sister and her niece had been at a sales conference and were heading home to the Manchester area.
The force said it was investigating the complaint.
A passenger, who asked for her name to be withheld, said there was no clear reason why they were pulled over on their approach to the M25 at about 01:45 BST on Thursday.
One of the women in the BMW said they were driving at about 30mph in a 50mph zone.
The family claim police first pulled them over to ask them if they were lostThe woman said they were first asked if they were lost. It later emerged the driver thought she was insured on her sister’s vehicle but was not.