Danielle Broadhead, 33, from died following the crash at 5.50pm on Monday, April 20 on the A637 Barnsley Road, near Flockton.
A Fiat Punto, travelling in the direction of Flockton from Grange Moor, left the carriageway and crashed into a tree.
Danielle sadly leaves behind her two boys Jaxon and Jesse, aged 22 months and seven years old, who were also injured in the accident, and her partner Steve.
They were taken to hospital for checks and treatment.
The seven year old was discharged following treatment to an arm injury.
The 22 month old remains in hospital for treatment to head injuries.
The injuries are serious but not considered life threatening.
A fundraiser has now been launched in Danielle's memory by a friend of her brother Luke Manning - who plays for Mirfield Stags Rugby team.
A post on the fundraiser said: "Sadly two days ago on the 20th April, Danielle Broadhead, Sister of Mirfield Stags player Luke Manning, tragically died in a car accident leaving behind her partner Steve and her 2 boys Jaxon and Jesse who were also injured in the accident.
"It is our aim to raise as much money as we can to help support Steve and the 2 boys.
"We would like to send our deepest condolences to all Danielle's family and friends at this awful time."
More than 70 people have donated to the fundraiser on GoFundMe already at the time of writing.
So far, £2,398 has been raised of a £5,000 target.
To donate to the fundraiser, click here.
Detective Inspector Paul Conroy from the Major Collision and Enquiry Team, said: “This was a truly tragic incident in which a woman has sadly lost her life and two children have also been seriously injured.
"Specially trained officers are supporting the victim's family at this time as our investigation into what caused her car to leave the road continues.
“I would like to appeal to anyone who saw the crash or the Fiat Punto in the moments before the collision or who has dashcam footage to contact us.
"Information can be given to MCET on 101 quoting log 1525 of Monday 20 April.”