Oh dear. Here's the problem. . . what they did was rude and improper. . . and not unlawful.
This is what cops do. All cops of every stripe. They lie, they make demands, they insult, they push buttons. All of it is in aid of getting you to give them evidence against you. It is permitted by law. Lying is permitted by Frazier v. Cupp, 397 U.S. 731 (1969). As cops receive more pushback, they become more sophisticated at lies and intimidation.
There's only one way to stop a cop on a mission. When "detained," give them whatever ID state law requires. My local law requires you to give your correct name when properly detained. OK, fine. I'll give them that. No ID document (unless I'm driving), and when they ask anything else, even how to spell my name, or to repeat it, nothing. Cops take huge advantage of the fact that Americans are very, very bad at SHUTTING THE FUCK UP!
We have the Constitutional right to refuse to answer questions (beyond identifying, which is a matter of local law). If you exercise that right, you'll win. It'll be 40 miles of bad road, but you'll win.
I don't mind them questioning a vet. First, illegal entrants serve in the military, and always have. Their service only occasionally "legalizes" them, and hasn't since at least World War II. And I know enough vets to know that, as a group, they have about the same criminal propensity as non-veterans.
See my "Trump Is Doing Something Good" thread for more comment.