Leonie Troke, 38, veered across to the other side of the road when she lost control of her car near the village of Great Wigborough in Essex in July 2015.
Her daughter Lucille was left paralysed from the waist down, Colchester Magistrates' Court heard.
Troke, of Wendover, Aylesbury, admitted causing death by careless driving.
The court heard the crash happened when she clipped the kerb or a rut in the road, tried to correct the steering but overcompensated, careering into a Vauxhall Astra.
Troke's two-year-old daughter was also in the back of her VW Polo but it was the older girl who was badly injured, also suffering injuries to her liver, spleen and lungs.
Jean Wilcox, 82, from Waltham Cross in Hertfordshire, a passenger in the Astra, died at the scene.
Troke, who sat with her head bowed during the hearing, was ordered to carry out 180 hours of community service.
She was also disqualified from driving for 18 months and told to pay Â£145 in court costs and charges.
Passing sentence, District Judge John Woollard told Troke: "I want to express the sadness that I have that nothing I could do today will have the effect of bringing Mrs Wilcox back, or repair the serious injuries caused to your daughter."
Outside court, the family of Mrs Wilcox told reporters they were happy with the sentence.
A driver who paralysed her five-year-old daughter in a crash, and killed an elderly passenger in the car she hit, has received a community service order.