Kirsty Parker, 34, from Denholm, died after her Vauxhall Zafira was in collision with a Peugeot 207 on the A698 near Denholm on Thursday afternoon.
Her sons, aged 18 months, nine and 12 were in the car at the time.
The 26-year-old male driver of the Peugeot was treated for "non life threatening injuries".
Ms Parker, a former waitress, originally from Kirkcudbright, was pronounced dead at the scene.
Her sons were released from hospital after treatment.
She also had a 16-year-old daughter.
Sgt Iain Blain, of Police Scotland, said: "This tragic incident has resulted in Kirsty's death and I offer my sincere condolences to her family.
"We are continuing to investigate the full circumstances and would be keen to speak to anyone who was in the area at the time and may have witnessed something, especially anyone who hasn't already come forward.
"I believe some people were assisting at the time of the collision and I would be keen to speak to them."
Police have appealed for anyone who helped at the scene of a fatal crash in the Borders to come forward.