George Zimmerman Fight -- Turf War Over Rented Home

George Zimmerman allegedly punched his estranged wife's father during a childish dispute over who had the right to be in the house -- the renter or the owner, aka George or his daddy-in-law ... TMZ has learned.

Sources close to Zimmerman tell us, George and his estranged wife Shellie Zimmerman have been renting a home from her parents, but ever since she filed for divorce they've been avoiding each other like the plague -- scheduling house visits ahead of time to keep the peace.

Must've been a snafu in scheduling -- because we're told George showed up Monday AM to remove some things, and ran into Shellie and her dad.

We're told the argument erupted when Pops declared it was his house, and George replied that he was paying rent ... and had every right to be there. The spat ended when Zimmerman allegedly punched Shellie's dad in the face.

Complicating matters was the fact George brought his new girlfriend with him. We're told she was waiting in his car while he went inside, and didn't get out until police arrived.

At the end of Shellie's 911 call you can hear her say, "There's a woman in there. Oh my god."

As for the identity of George's gf -- we're told she appears to be someone new ... NOT George's ex-fiancée, despite what reports are saying.