Good suggestions here.
I actually met a child just like that, at a park once....a girl, and my children and all the other kids, were avoiding her too and talking about her in 'icky' terms.
She has to be explained to... that her 'bossy' behavior is not good. And corrected right away. My Eldest sibling was like that, and even today as an adult... she is still real.... bossy. She has lost many friends that way and has had many childhood friend problems and angst... because of her MEGA bossy and arrogant attitude. So yes, it is good... to correct this in your Daughter.... when young. Otherwise, they develop an attitude later, that is harder to manage. Or they develop and attitude of 'entitlement.' And that is not good either.
Sure, it may be her age... BUT... in her case, it is causing MUCH problems with your younger child ( him crying because of it) and at the park even kids avoid her. So, yes, it is a problem....
The only way to stop it... is DO NOT ALLOW IT.
Put her in time out.
If she tantrums...SO what. You... have to be able to ride it out... and let the tantrum happen/tune it out... until she self-deflates. A child... WILL deflate on their own... ya know. AND talk to her....
I HATED growing up under the thumb of my eldest sibling. She was Bossy..... to the nth degree. As I said, even as an Adult... she is still that way. She has not learned.... to control it. And then wonders, why.... so many people avoid her or why she is lonely.
She also should be napping, as the other poster said.
She also needs repercussions for her bossying and tantrums
She also needs... correction right away. And I don't mean negotiating/debating/talking long winded to her... just swift action. Telling her RIGHT away "THAT is not acceptable. NO bossy talk.." then put her in a corner.
You ALSO have to teach your younger child, how to... stand up to her. To say NO to her... to tell you when she is being difficult and wrong... to stand up to her. DO NOT EVER, teach him that he 'has to' do what his sister says, just because she is older. That is the WRONG message.
Your Husband... also has to realize... how this is not good.... for any child.... for her or your younger child to grow up with a uber bossy sibling.
I HATED, as a child... being near my eldest sibling. She was so bossy.... so bossy. And it was not in a good way.
One day... your "Son" will grow up and be bigger and stronger than his sister... and if he gets mad enough... he will punch the lights out of her.
She has to watch out... she has a Brother.
My daughter has a brother. She likes bossying him too sometimes... and I told her, when he gets bigger he ain't gonna put up with her... that her behavior IS NOT CUTE anymore... and he will punch her, as boys are stronger. She didn't believe it... but NOW.... (my son is 4), my son DEFENDS himself against her... and she got nailed one time. And she cried. She learned, 'little brother' is STRONG. He has a very vocal voice... and physicality, that she does not have.
We don't encourage physical harm of course with our kids... but, one time my son just could not take it anymore, and he just punched my daughter. Boys. Will. One day.
In any case.. we tell my daughter, her being bossy is NOT cute, IT IS not acceptable, that brother is FAMILY... and she better stop it or she will be denied... everything anytime. My daughter was not real bossy, just sometimes, but I did not want her to turn into those chronically Bossy older siblings... like I had.
Tell your daughter, her behavior is not good. No one likes it. Her brother does NOT have to listen to her nor you nor anyone. That she is not allowed to do that.
When she is awful to her brother and he cries.... go to HIM, and take him away. Say to her "we are going over there. You cannot play nicely. He is hurt and crying. He does not want to be near you now. Do NOT boss him...."
You NEED to teach you son, how to stand up to her, and defend himself by speaking up.
Nip it in the bud.
all the best,
Susan