I would guess that your daughter isn't just "acting" sad when you've used your "not so nice" voice; she is sad. If an adult spoke to you that way, both in tone and content, you'd almost certainly have feelings about that – probably a mix of sad, dismayed, anxious, disappointed and/or angry. (Especially if the adult was someone you are dependent upon.) Kids are no different. Adults can sometimes hold all those feelings inside, but kids can't.
And all behavior can be seen as a means to get a need met, so the trembling lip is also that. But she probably doesn't set out to manipulate you, as in "I think I'll bug Mommy until she yells at me so that I can act sad and maybe get what I want (or so that I can have a melt-down, because it's so much fun to cry)." That would be manipulation. What is happening is probably much more spontaneous, i.e., arising directly from the dynamic.
I've discovered I dont "have to reprimand" a child when the dynamic is understood and handled proactively. My grandson, too, will ask and wheedle for what he wants. If I take him to a bookstore, for example, I know he'll want to head for the kids section where they also offer great kids' books, wind-up toys and stuffed animals. This is consumer heaven for a small child, who does not yet understand the concept of earning and budgeting.
So I decide ahead of time what will or will not be purchased, and I make it clear. I will also lead his thoughts well past the bookstore experience, to a desirable next activity. If he starts begging for a toy, I just calmly remind him that we're not there for a toy, but a book I had to pick up, and we are going directly to our next attractive stop. If he asks again, I will either ask him to repeat what the original terms are, or say, "Every time you ask, my answer will still be no. So, are you going to keep asking?"
There was a day when my grandboy was tired, had recently been spoiled by an uncle with no limits, and was terribly disappointed that he wasn't getting what he wanted, and started stomping and throwing things. I stopped everything, crouched down and held him, and said, "You are so disappointed. I know you want _____ very much. I would want it, too. In fact, I would want three of them. I understand. And I can't give you ______ because I need us to do ______ instead."
This was a technique I had just learned from the great little book How to Talk So Kids Will Listen, and Listen So Kids Will Talk, by Faber and Mazlish. And it completely changed my grandson's 3yo behavior. He realized I really did hear his wish, and wanted to give it to him, but could not. At which point, his whole demeanor changed. He was still disappointed, but willing to move forward with the next activity.
Since that surprising day, I have learned and used many of the wonderful techniques in that practical book, and my grandson is remarkably cooperative, even mature in the way he is learning to handle all sorts of potentially difficult situations.
I've also recommended How to Talk to a number of young families, who have been just as impressed as I was, in some cases with extremely difficult children with some rather scary behaviors.
