I agree with much of the advice-- half years are the hardest, sometimes.
Here are a couple techniques you might try proactively (before the meltdown):
(I'm going to copy some of your 'troubled times' here and make alternative suggestions)
"me telling her "no": Tell her what she *CAN* do. It won't work every time, but positive direction helps. (instead of 'you can't run in the house' try "You may hop like a bunny" or "lets make our feet quiet like mice"... keeping it playful also helps)
"me not understanding what word she just said": What works well for me has been "Tell me that again, please." When we say "I don't understand you" they immediately perceive this as a block to having their need/desire met. "Tell me that again" is helpful, so is "Okay, point to what you want/show me what you want" if you are still having trouble after she's repeated herself.
"telling her it's nap/bed time": This may be more a demonstration of her sadness about having to rest and/or separation. I like that you are saying "it's time for" as a matter-of-course and NOT asking "are you ready for" because that invites conflict. You might want to try offering a two-item choice immediately after making the bedtime announcement: "Do you want to sleep with kitty or bear?" "Do you want me to jump you into bed or fly you into bed?" The "How" choices (getting a choice in how we get someplace -hopping, jumping, being 'flown') help the child's brain/thoughts to move past digging their heels in about bedtime (or other necessary tasks) to 'how' they might like to do it, which gives them empowerment and all the good brain chemicals/signals that come with feeling capable and competent.
"telling her it's time to stop brushing her teeth": Here's what I would do-- if she just adores brushing her teeth, let that be her 'activity'... give her loads of time to do it, even at bedtime if need be. In fact, you might consider setting a timer for five minutes (or more, depending on how long she likes doing it) and tell her 'when the timer goes ding, I need you to come on out'... if she has 'too much' time on the timer, there will be no conflict. She'll be bored with it long before the timer chimes. And--once you have brushed them so you know her teeth are clean, get yourself out of the bathroom. Less attention is better in this case.
"me forgetting to let her help buckle the car seat harness": do you have two seconds to do it again? If you do, keep it playful: "Silly mommy! I forgot that buckle is YOUR job! I've got to try again!" If you don't, consider packing a 'quiet book' in the car that has a buckle for her to practice on. Distraction/redirection....
"not letting her go to every McDonald's we pass in the car (I have no idea where that came from)": Empathy time, but keep it short. "You think that's an interesting place, don't you? Now we are going to X". Matter of fact, you've acknowledged her feelings, and while I would encourage distract/redirect, I know that if you are driving, paying attention to the road is important. One mom I used to work with had a child who tantrummed in the car seat a lot-- she used to ask that child to help her watch for red, yellow, or green lights at different times, or ask them to 'tell me when you see a truck/bike/dog' etc.
"telling her we are out of something until I get back the store (i.e. juice, yogurt, crackers)": tough one here, but assertive choice is helpful. "I don't have that for you right now, you may choose X or Y" If the tantrum/bawling persists, take her to her room-- stay emotionally neutral and calm when you are doing this-- and tell her "come back when you are ready to choose X or Y" and leave. No more attention. Another idea would be to put a little of both choices already on a plate, so when she returns, she doesn't have to tell you a choice, she can have make the choice while she eats. This way, she's not choosing and changing her mind.
I would do as suggested and stick with one or two techniques at most. Personally, my experience as a nanny suggests that toddlers don't always really do well with rewards/incentives or sticker charts. Some do, but most don't. I find that our attention is the biggest reward and a very powerful teaching tool. This is why many parents suggest that when a baby/child bites a parent, for the parent to put the child down in a safe place and walk away for a short time.
I would strongly *discourage* you from trying to talk/reason/or love on a child during a tantrum. Certainly, lots of empathy for sadness or crying from pain/grief, but temper tantrums need to fizzle out on their own. When we stay attendant to the child while they are in a tantrum state, we are not doing them any favors because children do love an audience. When she's calmed down from the worst of it, you can offer empathy or move the moment along, depending on what the whole family needs at the moment.
There's a great book called "The Science of Parenting" by Margo Sunderland which you might check out from the library. It gives us a good view into the brain development of children and helps us to understand why they do what they do. Their brain really does process denial and unfulfilled desires/wants as 'pain' because it is less developed at this age, which is why you get the huge reactions. It sounds like you are doing pretty well all things considered!
