Shirley Anne Hunt, 44, and her children Ellie, nine, and Oscar, five, all died when their motorhome collided with a parked HGV in a layby off the A64 at Flaxton on August 24.
Her husband Craig, who was driving, and their six-year-old son Brooklyn survived the crash.
The family's names were not released by police at the time of the tragedy and inquests into their deaths have yet to open.
The children all attended Rockingham Junior and Infant School on the Wingfield estate in Rotherham and the school has now paid tribute to them.
North Yorkshire Police also revealed that their home had been burgled while Craig and Brooklyn were still in hospital, but a fundraising appeal launched by officers themselves raised thousands of pounds towards replacing stolen items.
A statement from Rockingham Junior and Infant School and Willow Tree Academy Trust said that the school community had been in “shock”, and paid tribute to the “kind” youngsters.
“Over the intervening weeks our whole school community has been in shock and devastated by the tragic deaths of the children and their lovely mum,” the statement said.
“Ellie and Oscar’s friends and teachers will miss them greatly, Ellie was a selfless, generous young girl who was a wonderful pupil and friend.
“She was passionate about her learning, especially for PE, and she was always willing to help her teachers and peers.
“Ellie will always be remembered for being a kind, considerate and enthusiastic pupil.
“Oscar was an absolute treasure, always smiling and a friend to all.
“He was a wonderful role model and was nominated as ‘Boy of the Year’ for his kindness, resilience and always doing his best in everything.
“Thankfully, Brooklyn and his dad, Craig, are recovering from their physical injuries but we will know that they will need every support we can offer in the coming months.
“We are working with our colleagues at Rotherham Council, South Yorkshire Police and other agencies to ensure that the best possible specialist support is provided to the family and to our children and staff, who we know are absolutely heartbroken by this terrible tragedy.
“Our thoughts and love are with the wider Hunt family and friends too, and with all those who knew, loved or taught the children.
“In the days to come we will find ways to celebrate the lives of these beautiful children and their mum and give everyone the opportunity to show their love and pay their respects.
“Until then our hearts and prayers go out to them. We ask for your kindness in giving us the privacy to grieve, so that our Rockingham community can come to terms with such a devastating loss.”