Ms Carter, who volunteers with Blue Cove Days, wrote on Facebook: "Juveniles ripped from their mothers, this scene, the mother and child are desperately trying to stay together."
The activist claims that the animals are then sold to aquariums and marine parks in Japan.
She added: "The price of a ticket and a day trip out to a marine park isn't worth this."
The video has been watched by more than 1.5 million people, since it was published on January 21.
Hunters have taken part in the annual Taiji Dolphin Drive between September and March since 1969.
But, numbers of dolphins taken during the hunt have decreased over the last decade.
In 2004, around 1,600 dolphins were snatched and by the 2014/15 season, around 750 were taken, according to the International Marine Mammal Project (IMMP).
The controversial hunt was brought to light in the 2010 film The Cove, which documented Taiji fishermen hunting dolphins.
The hunters would then try to sell the animals to aquariums for as much as £123,000, according to IMMP.
But in May 2015, Japanese aquariums decided to stop buying dolphins from Taiji.