They forced entry into a home in Cavalier Court, Balby, and began searching the property.
They got their hands on a quantity of jewellery while two children, aged nine and 14, hid from them.
The burglars, believed to be two men, discovered the children and then immediately fled the scene.
Police have now released CCTV images of a car they are tracing in relation to the incident, which happened on Tuesday, February 27, at 5.45pm.
A South Yorkshire Police spokesperson said: "One of the men is described as wearing pale blue jeans and jacket, with a scarf around his neck.
"Officers are keen to identify the owners of the car pictured as enquiries continue, as well as hearing from any witnesses who have yet to contact police.
"Do you live in the area? Did you see this vehicle?
"Please call 101 quoting crime reference number 14/35930/18.
"You can also give information to Crimestoppers anonymously on 0800 555 111."