"Disturbing the peace" is normally something that someone has to make a complaint about before the officer will respond. It's one of those catch-all pretexts that cops often use to justify an arrest where there is otherwise no grounds. The guy has a right to be a loudmouthed asshole in his own garage, provided that he's not disturbing his neighbors. Calling the cops "Nazis" across his own lawn is not a crime, and is protected speech under the 1st Amendment.
I have no idea why the woman was pulled over, but the officers seemed to be perfectly proper in their search of her and her vehicle, assuming there was reason to stop and arrest her. She was not "molested", as is suggested by the OP.
I feel the cops were provoked, but I don't see cause for them to enter his property or demand an ID when there was no apparent criminal act on the part of Mr. Loudmouthed Asshole Homeowner. The entry onto his property and into the enclosed garage, against his expressed desire for them to stay away, was a violation of the 4th Amendment. He had every right to keep on walking into the house, proper, close the door, and the cops would have no basis to proceed any further without a warrant.
That was an awful test of the Officer's patience and training, but not a good test case. I wish people wouldn't do this sort of sh-t.