Rather than focusing on how to punish/discipline, I'd first look at what is causing her to act that way... I'd make sure I'm treating her the way I would expect to be treated by another adult.
My ds always handled being told what to do, especially suddenly and without explanation, rather poorly. He's a pretty reasonable kid but I have to treat him respectfully for it to come out. So I wouldn't just say "it's bedtime now" or "pick that up now". He needs time to transition (not any more than any one else) and switch gears. I'd say "let's get ready for bed when you are done that game."
I'm not sure what set your dd off but frequently tweaking how you make requests can get a very different response from kids.
I learned growing up with siblings to never tell someone to do something unless you could/would make them. Chasing a kid and holding their door shut is no good. She's just going to get faster, bigger, and stronger. Also, your getting physical with her in that way makes it easy for her to justify being physical back.
Then there are some kids that have food sensitivities, aren't getting getting enough sleep, or have difficulties regulating their emotions for whatever reason. It's hard to even guess what might be going on in your household and what might help without more info. What to do really depends on why she acts the way she does.
Mom to unschooling 4everboy since 8/01