GAAAHHH. We have had this problem off and on since our kid was 3; he's now almost 9. It's so frustrating! I understand completely how much it wears on you even though it sounds like such little problems--it's the non-cooperation that hurts my feelings and seems like he doesn't realize I'm the parent (why doesn't he feel the fear of disappointing his parents that seemed to be instinctive to me when I was a child??), plus the cumulative effect of being defied over and over again. So, I don't have any foolproof strategies, but these are some things that help when we make ourselves do them instead of just shrieking the first thing that comes to our frustrated minds....
Say what you want, not what you don't want. Instead of, "Don't pour it out," say, "Keep it in the cup." For something that's a persistent problem, give the positive instruction before the negative behavior begins. For example, I used to get frustrated that my son would fill his cup completely with water, brush his teeth, use a little water for rinsing, then dump the rest of the water down the sink and waste it. I tried, "Take only as much water as you're going to use," but that didn't work--he really liked filling the cup to the top. So I started saying, while he was still brushing, "Give your extra water to the plant," pointing to the potted plant that's next to the sink. Now he usually remembers to pour the rest of the water into the plant pot. (I have to remember not to water that plant myself--it's getting more than enough from him!)
Say, "When...then..." Instead of, "Don't turn on the radio," say, "When Daddy gets up, then we can listen to the radio." Instead of just, "Pick up the markers," say, "When you have picked up your markers, then we can go to the park." This lets her know that she WILL be allowed to do the thing she wants to do, just not NOW.
When she does something that you have previously, recently told her not to do, impose a logical consequence immediately. Don't give a warning. It is a lot easier to stay calm when you act quickly instead of letting repeated noncompliance get to you. For example, she's drawing on the wall, although you told her yesterday and last week and many times in the past 3 years that drawing on the wall is not allowed, so you know she knows it's not allowed. Take the crayons away. Say, "Crayons are only for drawing on paper. Because you were drawing on the wall, you may not use the crayons any more today." Put the crayons out of reach. If she begs for them back, repeat, "Because you were drawing on the wall, you may not use the crayons any more today." Next day, when she asks for the crayons, say, "Tell me how you are going to use the crayons." She should be able to explain that she will draw only on paper. Give a very positive reaction, "That's right! Crayons are for drawing on paper! Let's get out the paper." Get her all set up to do it right, then get out the crayons.
At night when you apologize for behaving badly, is she also apologizing for HER bad behavior? If not, I think you need to find a different way of discussing this. I agree it's important to model responsibility for our actions, but you're right that doing this frequently--if it's one-sided--can give her the impression that Mommy getting mad is the real problem here, and she'll focus on that rather than on changing her behaviors that trigger you. I feel more successful with apologizing right after spinning out of control and then explaining: "I'm sorry I yelled. When you waste water, I feel angry. We are lucky to have clean water to drink. We need to use it wisely." I try to just *briefly* state the triggering action and then keep the focus on how *I* feel and what *we* do when we're doing it right. If you go on and on about what your child did wrong, it starts to feel like a harangue that's easy to tune out, plus you're emphasizing what you *don't* want. But it's crucial to say *something* about why you were mad. The book Parent Effectiveness Training is an oldie but goodie filled with great examples of how to do the "When you... I feel... because..." thing well.