Just keep standing your ground and never give him. Eventually she will understand that she won't get her way and she has to listen but it is very important you never give in. If you do, she will know that she can get her way when she acts a certain way.
First of all, pick your battles! I've learned (Ryan is 3) not to go crazy over the little things. Realize why she wants or doesn't want something and see if maybe there's a change you can make. Like does she have to sit in a high chair really? Can she just sit at the table?
Second, I don't think her putting her toys in time out means that she likes it she just mimics what you do. It's normal. Ryan does the same thing.
Don't argue with her just stand your ground.
When she does t want to put her shoes on to go just say "ok then you can stay here alone mommy is going " I've had to do that with Ryan. I tell him he can't go if he doesn't do whatever it is I need him to do.
Is she getting enough attention? She may be jealous over her brother? Is that when this started?
Try to make her think the stuff you're asking her to do is her decision and maybe give we options like "ok we need to go do you want to wear the green shoes or te blue shoes" or something to that effect instead of demanding she do things all the time. She's at a very independent age and they want to decide what they do and what they don't do.
And there's nothing she likes to do that you can take away? Does she like to go to the park? In the morning tell her if she's good you will do whatever with her and if she acts up then you simply tell her ok if your arent going to so such and such you don't get to do whatever.
Redirect dangerous behaviours
Ignore inappropriate behaviours
Praise good behaviours
Pick your battles
For example: Going out - lead up to it. Tell her in the morning that you will be going out in the afternoon (or whatever), give her another warning at lunch, then another an hour or so before, then countdown from 10 minutes. In the 30 min or so before you are going out, make sure that the television isn't on, that she isn't involved in a game or with toys that can't be taken with her. Another option is to keep a backpack filled with a couple of snacks, books, small toys, etc. ready to go.
Ask her to put on her own shoes, like a big girl. Ask if she needs help or if she can do it by herself.
Encourage her independence, it sounds like that is what she wants.