Prince, who has been brought back into the side after five Tests on the sidelines, is said to have been involved in an ongoing verbal slanging match with Test batsman AB de Villiers and spinner Paul Harris this week.
Witnesses said it became heated and abusive, although no reports were made.
Prince plays for the Eastern Cape Warriors and the other pair for the Northern Titans.
It is understood Prince had the Proteas acting captaincy taken from him a day after he got the job.
Sources close to the team said Prince, who was upset at being brought back as an opener, demanded the decision be reviewed and that as he was acting captain he should have a say in it.
Cricket South Africa chief executive Gerald Majola was outraged at the demands and Prince apparently was removed as captain and replaced by Jacques Kallis.
Mark Boucher had acted as captain during the second Test, replacing Graeme Smith who had broken his hand.
Neil McKenzie filled in when Smith was injured in Sydney but was not asked to do the job because it is believed selectors had already decided to drop him.
Smith is furious at the situation and has fallen out with selectors, but says he will be in the rooms during the third Test, starting tomorrow, to guide the side.
South Africa is down 2-0 in the series and had been confident of a win which would have gained it the world champion title.
Prince aired his displeasure with selectors early in the series, claiming he had only discovered he would not play in the first Test when contacted by a journalist.
He has refused to comment on the captaincy controversy, but is said to be furious that de Villiers, who has opened before, stays at No.5, which was Prince's spot until he broke his hand before the first Test in Australia.
Prince and newcomer Imraan Khan will open the batting in the knowledge that one of them will be dropped when Smith returns from his broken hand.
Yesterday, coach Mickey Arthur called on the players to come together as a team. (ANI)