Nothing! Nothing at all is wrong with your child. She sounds like a great little girl to me and you sound like you're doing alright with her. But I'd like to offer some advice.
I worked in daycare for 7 years and I've had kids like yours. Now I have my own wildly 3 year old who is strongly opinionated and it the same rodeo.
First off, pick your battled at home. Is her hair in a pony tail is really with the fight? And punishments after the fact aren't super effective on kids that young let alone for things like "juice at dinner is a treat for when you don't get in trouble". It's as confusing to her as it would be the IRS telling you no binge watching anything on Netflix because you're behind on back taxes payments this week. She doesn't fully make the connection from her folder stamp to all those punishments. She can't, not really. Save that for a year or two down the line.
She sounds like she needs a day care that can offer her guidance and correction at a different level because no time outs and making other kids work around her hasn't done her any favors. Sometimes, kids need a break away to regain themselves, even if they're not in trouble, just over whelmed. Maybe one that can better cater to her preferred method of learning and engaging as well. Some kids just play differently and need to feel their emotions differently so they can have a shot at adapting to a classroom routine.
Next, her fucking daycare kept her in a class full of peers that weren't engaging to her? No fucking shit she started to lash out. She probably picked up a lot of bad habits from there that were reinforced until she moved to somewhere else.
Also, does your daughter have a passion? A couple of favorite things to doto express herself, she'll do every day if allowed? For my son, it's drawing/coloring cut/pasting papercraft, for my daughter, it's play doh and "snake" families with string and thread. Let her do them! Every day. And never take them away. Even if my kids are beyond in trouble, I always let them have their ability to express themselves for at least 45-60 minutes a day. That's her create play and how she reflects on and figures out things in her life. Maybe play mommy and daddy or teacher and student with her dolls with her to get that going. Make the plot fanciful and magnificent but the behavior of the characters kind and polite (we're on the moon and moon fairies have invited us to lunch! Lets wash out hands and tell them thank you. Oh will you please pass the moon cheese?) Anything that reflects how she understands the world is great but she might need help learning how to play like that if she doesn't already.
Go ahead with whatever therapy to get her evaluated. Of course I could be completely wrong because I've never met your child and I have my own biases and hold the policy that truly "bad" children are very, very rare. Kids who don't do well with one method of care deserve the chance at another and another with a few professional diagnoses before they should be written off as "something wrong with them".