Fight Over Monica Burgos' Body

There's a family fight brewing over plans to cremate Monica Burgos Beresford-Redman's body ... TMZ has learned.

Sources tell TMZ Bruce Beresford-Redman never authorized cremation of Monica's body, contrary to what Monica's family is now alleging.

We're told when Bruce was being interviewed by Mexican authorities, they told him he must arrange for transportation of the body to the U.S. -- but that was the extent of it. We're told Bruce was asked to sign a document, but he claims it was about transportation, not cremation.

Sources say Bruce gave his credit card to one of Monica's sisters to handle the transportation issue... and that was it. But Carla Burgos tells TMZ her family never received a credit card from Bruce -- her family took care of everything.