In the film they can be heard laughing in the background despite the children being reduced to tears. It was discovered by chance and passed onto social services.
Zara Care, 29, Carole Olver, 48, Serenza Olver, 29, and Danielle Olver, 19, from Plymouth were given 12-month suspended sentences after they earlier pleaded guilty to child cruelty charges.
Judge Francis Gilbert described the film, lasting eight minutes, as "shocking".
"You were cruel, callous, clearly causing the children to hurt each other for your own pleasure," he said while passing judgement at Plymouth crown court.
The boy, wearing just a nappy and T-shirt, was cheered for using a magazine as a weapon and hitting the girl around the head. At one point a hairbrush was thrown into the room to use in the fight.
David Gittins, for the Crown Prosecution Service (CPS) Devon and Cornwall, said: "We in the CPS had no hesitation in prosecuting this case. Anyone who saw the video footage, shot by the mother of these two children, cannot have failed to be shocked by it.
"In many years of prosecuting child cruelty cases, this stands unique, defined by the cruelty and callousness shown in the evidence. For children in a family situation that should be protective and loving to be made to fight each other for the enjoyment of adults and to be verbally abused when they refuse is utterly unacceptable."
Click here to run an energy price comparison, and see if you could be paying less for your gas and electricity.