Claire Throssell's ex-husband Darren Sykes lured Paul, nine and Jack, 12, to the property in Penistone on 22 October before setting fire to the building.
A charity appeal in aid of Ms Throssell has been set up with the aim of raising enough money to help her restore the property and sell it.
Campaigners have so far raised around Â£8,000 of a Â£50,000 target.
Ms Throssell said: "It's just amazing, the people are just awesome and I just can't believe that so many people are carrying that love for my boys.
"It's keeping their memory alive. They were the best part of me, they were my life and it's lovely that people love them for who they were."
Rebuilding work has begun at a house in South Yorkshire where a man killed himself and his two sons in a fire.