It isn't illegal to be rude, but the cop also doesn't have to let you off if you are being an asshole. She broke the law and he was going to be nice and let her off with a warning. Instead she was combative and he decided not to.
He asked her nicely to put out the cigarette and she essentially told him to fuck off she can do what she wants. Nobody has to sit there as inhale your shitty smoke.
Cops can order you out of your car for no reason once you got pulled over. It is definitely not false arrest. And I think the cop had totally reasonable grounds to make her get out.
Would you sit there and get shittalked while someones blowing smoke in your face because she has an authority/anger problem.
Being a dick to a police office who can still use his discretion to let you off is a really dumb move.