Jordon Hudson Impossible to Work With During Bill Belichick Interview, Sources

Jordon Hudson went completely off the rails during Bill Belichick's CBS interview -- to the point where she stormed out of the room and delayed shooting for 30 minutes ... sources familiar with the situation tell TMZ Sports.

Belichick agreed to do a sit-down with Tony Dokoupil of "CBS Mornings" to promote his new book, "The Art of Winning," but it turned into an L -- at least PR-wise -- when his 24-year-old GF interrupted the interviewer, asking Bill how they met.

We're told outside of that baffling moment that made the final edit, there were numerous other instances of Hudson butting in -- even when the legendary coach was answering questions about football, she would stop and correct him.

Our sources say Belichick only arrived at the interview with Hudson -- no one from his publishing company, the University of North Carolina, or any other rep was with him ... which was a bit of a head-scratcher to CBS producers on set.

At one point in the Q&A, Hudson got so heated ... she stood up and walked out and wanted BB to follow. It's unclear if Coach agreed, but the blowup delayed the whole interview for about half an hour.

We're told once things calmed down, Dokoupil -- who was "spooked" by the whole encounter -- elected to wrap up things quickly and end the awkward experience.

As for how the dumpster fire of an encounter got edited -- we're told the higher-ups at CBS News and Sports had to get involved to figure out how to salvage it ... and while a second interview was scheduled to go down at a later time, it was ultimately scrapped.

The whole ordeal also isn't sitting well with Bill's employers -- we're told folks at UNC are now concerned about Hudson's influence on Belichick's tenure as the head football coach in Chapel Hill ... especially with her, essentially, taking on a role as his manager.