There's a book called The Explosive Child by Ross Greene that will help. My 5 year old is the same way with ADHD mixed in. Once we got the anger and frustration under control then we did all the other testing and trying to control the ADHD until we finally had to choose between homeschooling and medication.
The best thing to do now is to remove the baby from her grasp. That means keeping him with you at all times and setting up a baby gate to keep him away from her room. When DS#2 is on the war path he's gated off so that he can only be in his room and get to the boys' bathroom. My two year old cannot get past the gate.
The next step is to develop a growl and a poker face. Show no emotion but lower your voice to the range of a feral animal protecting it's young. Talking through clenced teeth is a good start.
As far a public situations, she can't go. Yes that means no church. No trips to the store, restaurant, or babysitters. She's grounded and unfortunately so are you. Once you're "working the baskets" from The Explosive Child then you can venture out. When she melts down in public you can calmly tell her, "I know you are frustrated and I except that you are going to have a meltdown, however if you do anything more than cry we will go back home and you will go to your room until you have managed to get over this" I've done this in the grocery store, library, church, even at school.
Now school is another story. If you don't have a teacher that is willing to "work the baskets" with you you're not going to get it under control there. The best you can do is send home a daily report and you can reward or punish her accordingly
Here DS#2 gets a smiley face for every half hour he can control himself. Naughty habits like making noise, sticking out his tongue and saying mean things earn him a straight face =/
Acting out and doing physical things like tearing things off the wall, knocking over chairs and such earns a sad face.
When he brings the daily report home I post it on his mirror in the entry way. For 12 smilies in a row he earns a reward, his teacher gives him a sticker for smilies 90% of the day. He has the potential of earning 4 rewards a day, two-12 in a rows and one for making 90% of the day and a Special bear for 100%.
6 special bears earn something extra special~bonfire, staying up all night, scrapbooking, Playtime Plus, fishing with daddy
6 in a row or making the goal for the day earns something back~activity, privileges, room decor, freedom from his room.
There have been a few weeks when he was in his room everynight. He's even had nothing but his furniture, no pillow, sheet or blanket. Eventually he got the point and started earning things back.
Hang in there