Terrible threes

The terrible twos have nothing on the tantrums that a three year old can throw. They're bigger, stronger, and more articulate, making their tantrums an extraordinary sight. They are crafting their manipulation, testing boundaries, and exploring the limitations of their vocal chords.
It's embarrassing and disheartening. It makes you question your ability to be a mother. Have I been too lenient?Too strict? Have I said all of the wrong things?
I start making a list of every bad parenting move I've made and of every change that I will enact from here on out. I should know that she's three, that I've done everything a good mom should do, said all of the right things, with only a few mistakes (which is normal).
It's difficult not to notice every parent and child in the store (when these tantrums happen in public). They're children seem so calm, peaceful, and well-behaved as I hurriedly push the double stroller and pull the cart it the three year old to the nearest exit.
On the long car ride home I can't help but wonder if all of this screaming will negatively affect the twins. Do they hear and understand and feel the stress and panic?
Once we're home, she goes to her room and we remove the most precious of toys. But it boggles my mind how quickly everything is forgotten. Within minutes she's back to normal, playing, laughing, and hugging her poor mother.
I want to be like that. Forgetting the rotten things, moving on, and genuinely returning to love like nothing ever happened.
In the end I find out she's not feeling well. I should have known. Her cheeks were red (usually a sign for Adi), and she didn't eat one bite if breakfast or lunch, and now I come to find that she's fallen asleep.
I need a clear discernment as a mom. To see the cues and head things off at the pass, and return to love just as quickly as a child.