's divorce case was front and center in a Miami courtroom Wednesday, and Joe's lawyer made it clear ... there's gonna be a dogfight over who hears the case -- an American judge or a UK judge.
The stakes are extremely high ... if an American judge hears the case it gives Joe a huge home-court advantage, and the reverse is true if the UK judge gets the case., made it clear ... based on his exchanges with Sophie's counsel, she says their family had become UK-based so the divorce should be handled there.
Sophie's lawyer did not directly respond, but our sources say that is exactly what's happening in the case. If a UK judge handles the divorce, it's likely the primary residence of the 2 kids will be there, and Joe is not down with that.