Myriam Lebrun, 37, veered off the Long Island road and crashed into a tree. Her Honda Accord burst into flames, killing her, along with her mother, Yolanda Moise, 69, and children, Marquis Jeanty, 14, Marcel Jeanty, 9, and Kayla Jeanty, 8.
Police say they are working to determine the cause of the crash, which occurred around 11 p.m., and are considering whether alcohol or speed was a factor.
The family was apparently returning to their home in Brooklyn from visiting Lebrun's sister in Brentwood on Long Island. Relatives told investigators Lebrun had a few drinks throughout the evening, and didn't eat, but said they did not believe she was intoxicated.
"She wouldn't endanger her family," said Christine Moise, 20, a cousin. "She just wouldn't."
"I can bet my life that she wasn't drunk," she said. "These kids were her everything. Her kids were her life."
Others said the road -- not Lebrun's driving -- was to blame.
Area residents say the stretch of the Southern State Parkway where the crash happened is better known as "Southern Snake Parkway" because of its dangerous curves.
"I try to avoid it at all costs," Matilda Mortar told WCBS Long Island.
"When I drive on the road, I see the trees with those little plaques on them," added Anthony Vella. "So many people go off the road and hit the trees and die."