For me it's not a question of not answering back and obeying out of fear. I think individual women can do whatever they choose, provided they are aware that the police have good reasons for asking you to comply with specific instructions, and refusing to cooperate is far, far more likely to have negative consequences for you than cooperating. The law doesn't stop being the law, and nor are you exempt from it just because there have been a few high profile instances of police officers abusing their position. It's this indignant "I don't care, I am above the law and I will not comply" attitude that is risible. You are not, and you are going to receive an extremely rude awakening one day if that is your consistent attitude whenever you encounter police. If you are fortunate like OP, the police will understand and exercise a degree of discretion. If you are less fortunate, you will find yourself arrested and charged, needlessly, and entirely because of your own sanctimony. It only takes one tired, worn out officer who has been having a difficult day to think "yup, screw this, not putting up with this nonsense".
As I've said earlier in the thread, I'm no stranger to confrontations with the police, but personally I do not share the mistrust that many women in this thread are voicing, as understandable as it is. I view risk in a very pragmatic way, and I don't perceive individual police officers as a potential risk to me because a few might have behaved inappropriately, because for every single example of that, there are an order of magnitude more examples of exemplary behaviour that go unreported, so the reality is that the personal risk to me is so vanishingly small that I can't give it any headspace. It's a bit like refusing to fly in the immediate aftermath of an airliner falling out of the sky, when rationality tells you that is the exception and hundreds of thousands of flights are completely perfectly safely for every instance of one going wrong. There are people who are irrationally scared of flying of course, but these are not the people I'm describing. It's about ability to rationalise risk and put things in perspective.
As for asking "what can the police do to restore trust?", perhaps part of that would include the police explaining exactly why they might ask someone to comply in a specific way, explaining why it isn't realistic for you to remain in your car to perform a breathalyser test (some regional forces might do this from time to time, but its far from best practice and I suspect it only happens in cases where the officers involved are pretty much certain you aren't under the influence in any case), and why it isn't realistic to 'offer' to drive yourself somewhere.
If they could do that, perhaps people would regain some perspective and realise that an attitude of non-compliance is not going to get you very far when the police have far more options than you do, and they also have the law on their side. You are not going to redress a power imbalance by trying to chuck around weight you don't possess in the first place, and individual officers will not, and do not take kindly to members of the public trying it on when they are just trying to go about their job.