She is 3. They do this.
3 is a harder age, than 2.
They are not yet a "big girl", and yet still babyish. It is a "cusp" age, thus it is full of difficult moments... for the child.
Their emotions, are not even fully developed yet, nor their ability to handle it.
So they need to learn coping-skills. Which is something that is taught to them. So that they learn emotional articulateness.... so that later they can navigate themselves. And it also encompasses learning boundaries.
One thing is that I have always from 2 years old, taught my kids about emotions/feelings and how to express it AND to say it, in a palatable way. I "allow" bad moods, because even adults get that way. But that they can tell me how they feel, in a nice way. My son for example, if frustrated, will actually tell me "I'm frustrated... leave me alone now..." or he will go and deflate himself. Then when he feels better, he will tell me that too. Then he hugs me. I am proud of him. Good or bad, it is teaching them HOW to manage & express, their feelings and frustrations. Too.
If my kids get tweaked/obstinate for no reason or are unreasonable, then I simply tell them acting like that will not make me cooperate. And that they "redo" their actions. Thus, it ALSO teaches them "problem-solving" and there are OTHER ways of doing something or saying something. I will give them a chance, to correct their actions... I say "redo that..." and they will often do it. They do know, how... because we practice different ways of doing things. Not just "my" way. Only.
AND, if I know they are "trying their best..." then I am satisfied with that. I do not expect absolute "perfection" in them.. but that they "try their best...."
Also, no, don't give in to unreasonable demands. I would NOT have gone to go back and wash her hands. Too bad.
A child WILL deflate on their own... just ignore it. Then once they stop... then tell them "great, you calmed yourself down..." then go on with things. Or tell her, yelling won't get her anywhere.
Also, your girl seems tired. Does she still nap???? A child this age, does need to nap. When my daughter is tired, she gets like your daughter... moody/fussy/emotional/tantrum-y. When she does nap, she is much more even keeled and happier and pleasant.
The thing is: a child will get frustrated. SO, teach them how to manage frustration... and give them skills to help them. And practice it. Don't just "expect" the child to automatically KNOW how to handle it. They are young, they don't know how. And sometimes they don't even know how to express it nor how they are feeling. So teach them about feelings/the names for it and how to say it. Then as a TEAM... that you work on it or problem solve it.
all the best,
Susan