Oh, poor lamb. She's 2, with a brand new brother, and a brand new sense of independence. Hard for both of you.
I wouldn't let her down from the table at dinner. Encourage her to stay and chat. Give her attention. Put something you know she likes on her plate, even just a bit of bread and butter, so she'll eat that.
The screaming is awful, I don't know what to do about it.
How much warning does she get for transitions in her day? How well do you explain the structure of the day ahead? I would suggest visual aids and a walk through in the morning. Teeth is non negotiable but you can try things like the Hey Duggee tooth brushing song, or the Oral B Disney app, to encourage and make it fun. Don't fight over coats, let them get cold. Play games, be silly - put her shoes on her hands, run the hairbrush down her legs.
Can you get a toy car seat and let her buckle in a favourite Teddy, and sing to Teddy so that Teddy will sleep in the car? Or let her choose some songs to listen to before she gets in?
What is the bedtime routine like?
I remember how hard the age is, but it does sound like she's desperately trying to grab your attention. It's easy to say "you're a big girl!" but really she isn't, she's barely more than a baby, and she'll see how nice life is for the actual baby and want to be little. So many cuddles and so much patience.
Always have wine ready.