Law enforcement sources tell TMZ ... Ella -- who's Second Gentleman Doug Emhoff's kid -- was out in the Tribeca neighborhood of NYC Tuesday afternoon, where she was grabbing a bite at a restaurant ... all while her Secret Service detail was standing guard out front.

We're told while she was inside, one of her agents -- who was dressed in plain clothes -- had an altercation with what's been described to us as an "anti-police watcher."

Basically ... this guy goes around and makes a fuss about NYPD parking placards given to law enforcement agencies ... so they can park without having to circle the block a ton.

In this case ... our sources say the dude in black came up and started getting into it with the Secret Service agent in blue you see in the video ... apparently not realizing he was an agent ... assuming he was a cop abusing his parking privileges.

During the argument -- part of which was caught on video and obtained by TMZ, the guy ripped a plate off of one of the Secret Service vehicles ... and that's when cops were called.

You see the dude led away in cuffs. Our sources say he was arrested, but it's unclear what he was charged with.

An eyewitness tells us Ella and a friend -- who were inside the entire time while this was all going down -- were rushed out and placed in one of the SUVs, which you see in the video.