babies and kids go through developmental stages... and this includes cognitive and physical changes. Most of which is normal.
"Emotions" in kids this age, is NOT even fully developed yet.
They don't even have deductive and inductive logic fully developed yet. Not even some adults do.
They don't even have socialization fully developed yet. Nor communication. Nor vocabulary. Nor do they even have the ability to know themselves or how to tell you what they are feeling nor the ability to self-reflect and analyze their own behavior and then tell you.
They don't even know when they are tired and need a nap and are hence fussy. They don't even know how to tell you they are hungry, need a snack, or else they will be fussy.
They don't even know how to handle frustration. They don't even have coping-skills yet, because it is taught and per cognitive development.
She is only 2.
And at 3 and 4 years old, it actually is harder. Per age stages.
Kids this age do not even have, fully developed impulse control.
Thus, safety proofing a home is important for these ages.
Even if a kid was raised in a cave by themselves, they would go through developmental age stages and changes in cognition and physical changes too.
Kids are undeveloped.
Not fully developed.
And teaching them concepts, takes all sorts of approaches. But if a child is only "punished" without knowing why or not taught concepts, they still will not learn, the thought process to it.
It takes parental... guidance.
And, kids do things over and over and over.
Just one session of a 10 minute time-out, is not going to extinguish... a behavior.
Some adults still act that way, even if they are grown up.
Time outs alone do not get any message to the kid.
Nor does it work if the child simply does not have the ability or cognition to fully control their cause and effect behaviors.
Guiding and teaching a child, takes, years.
Everyday.
And, for a 2 year old, they can get territorial. Some kids don't like other kids in their home. 2 year olds don't even know how to "share" yet. They aren't even fully socialized. And they do not play interactively yet. They do what is called "parallel play" at this age.
It is developmental, based. And per age stage.
And when she is doing something harmful to another, you remove her.
TELL her why.
By now, the words "danger" and "stop" and "no" should be understood by her.
Maybe, get your daughter in a Preschool program. Just part-time for half days. So that, she is around other kids her age and learns socialization and group dynamics.
At this age, they start to need more... interaction. And with others their own age.
Even a child who has a baby sibling, can get "tired" of being around a baby all the time...and the crying of baby. A toddler child, starts to need their own activities and same-age things to do.
Does your daughter nap?
Sounds like she needs to.
Over-tired kids, can act like that too. They get unglued.
And if going through a growth-spurt they need snacks and good meals.
Or they get fussy.