[Dallas59]

The relevant Supreme Court cases here is Pennsylvania v. Mimms, the TL;DR of which is that orders given by an officer to the driver in a traffic stop must be followed to maintain the safety of the officer (like danger from oncoming cars while standing in an active roadway). A further Supreme Court case (Maryland v. Wilson) extends the officer the right to do the same thing for both the driver and their passengers. There's also this particular Texas law:
Texas law: Sec. 542.501 - A person may not willfully fail or refuse to comply with a lawful order or direction of...a police officer
So when he did order her to put out the cigarette or step out of the car, she was obligated under Texas state law as well as US federal law to obey his directions. He doesn't have to give a reason, and disobeying a lawful order can quickly become a reason for an arrest, even if it seems crazy.
Basically, if you or any motorist is ever pulled over for a traffic stop, this description quoted above is fairly accurate in any part of the country.
Basically just be respectful, don't be a smart ass, and if you're given an order from a LEO, follow it calmly and politely. If it's something you don't agree to, but it looks like it's probably going to happen anyway, let them know that you don't consent to whatever it is, but follow the order anyways.

[TheConservator]

I hear what you are saying. Although I wonder how the order to put out the cigarette had anything to do with officer safety.

Yet, it seems clear, to me at least, that those orders to put out the cigarette and then get out of the care were the direct result of her following his express direction to explain what’s wrong, and him simply not liking the words that came out of her mouth—even though she directly and honestly responded to his question. I don’t think cops ought to be able to penalize people for doing exactly what they are ordered to do, or simply saying what they are thinking.

[T2lanelwr]

Good point. However, there is also a real issue as to whether the officer violated the Supreme Court’s ruling in Rodriguez vs. U.S. prior to giving the “lawful order” to put out the cigarette. From what I saw on the video, the officer returns to the car, and only has to give her the warning he had written up. Instead, he engages her in conversation, asking why she is upset. At that point, he is unreasonably, extending the stop in violation of Rodriguez. This infraction occurs prior to giving a “lawful” order. So it seems to me Rodriguez comes into play first. I think there is a pretty clear Rodriguez violation. The second issue is whether the question “ would you please put out your cigarette?” is an actual “order” it is clearly phrased as a question, to solicit a response, and is said during a conversation which potentially violates Rodriguez. I agree that he has the right to order her to put out the cigarette, if it was an order and was given during his mission. Rodriguez is pretty clear, that an officer may not delay his mission during the traffic stop. He clearly, did this when he engaged her in casaul conversation prior to issuing his warning. All, in all it was really poorly handled by both parties. There is also the issue of why the officer makes no mention of the lawful order to put out the cigarette in his report or to his supervisor. This could arguably be because it was not a lawful order. In either case, interesting issues in this case.