My 2 pence on sibling rivalry!!

It's a very tricky situation for any parent to be in!!!
When my 3 year little Amu old tries to boss over Gowri, I am fine most of the time, assuming that's a common thing amongst siblings, but when it goes overboard, then I take a firm stance against it and it's almost always Amu who is at the receiving end.

But I have my own concerns over this from time to time. Since I am home currently, I tend to think a little more about it.  My questions range from, am I doing the right thing in giving her a strict warning or giving her a time out? Am I being too harsh on Amu, she is after all not even 3?
Is this a normal  behavior among siblings? Is it a little more in this case as they are both girls?
Am I alienating her against me? Will she have negative thoughts about me because I am punishing her?
Will they ever be those share all kind of sisters that I see my friends to be?
It's an endless list.
Amu seems moodier than usual these days.
I hope everything will settle down soon.
I can just wish for a good relation and try to be a good mom.  God help me and guide me.