The woman then screams 'Hold my daughter!' and pushes her double stroller to the side as the two men jump around each other with their fists raised.
As the two start punching each other children are heard crying in the background and another woman enters the scene yelling 'Stop it! Stop it!'
A mother in a motor chair then rolls in between the fighters in an effort to stop the violence but she ends up getting hit in the process.
But the man in the pink shirt is still angry with the woman in the white shirt and follows her, punching her in the face and pulling on her long braids.
Concerned bystanders are heard shouting for the fighters to stop and one woman yells 'Call security!'
Finally the fight is broken up by men standing nearby and the man in pink seems to go on his way.
Then the woman in white with the braids gets into a tiff with a woman in a brown shirt, pulling on her hair. As the two fight they push the elderly woman who was sitting in a motor chair earlier to the ground.
The man in pink returns and says 'You got what you wanted...Let's go momma' referring to the woman on the ground.
Then he continues to slap the woman in braids, swinging her around until she falls to the ground.
'I don't care about no video! I'm ready to go to jail tonight' he yells, his pink T-shirt visibly torn up from his fight.
Bystanders then flock to the woman sprawled on the ground and keep the man in the pink shirt at bay.
Then the man in pink starts to hit the woman in brown saying, 'You hit my momma?' and throws punches to her face and body until she falls to the ground and pulls her hair.
Three men then pull him away and bring him to the ground and keep him there until Disney guards arrive on the scene.
Anaheim police are investigating the incident after it was flagged to them Sunday and are interviewing family members portrayed in the video.
Officers say none of the victims were cooperative and were escorted away from the park.
Authorities say they are pursuing a criminal case.
Disney confirmed to DailyMail.com that the brawl took place on Saturday and said "We do not condone this behaviour".