Honestly, I don't think much you do at home has an impact on a child this age in the classroom. 95% of the work has to be done by the teacher, at the moment. If the time out isn't working and your daughter is returning with a triumphant (?) smile on her face, then the teacher needs to do something else. So some of this is classroom management - but as a former teacher, I can tell you that one disruptive kid in a big class is a huge problem. Even when I had small classes, I had 2 kids over the years who just had to be sent to the office rather than disrupt the entire program and delay the education.
I would find out what happens in the principal's office. Is she feeling like a big shot there? What exactly is she doing? Is there some boring busy work she can be assigned? Either that or constantly being ignored. It's inconvenient, but if she is denied the privilege of going to the girls' room alone or going to assemblies, that would be good. I know she has to be supervised wherever she is, but it shouldn't be with anyone fun. And if she has to repeat kindergarten, so what? She's probably too immature to move on anyway, and this is the time to deal with it.
If riding the bus is a privilege and fun, then you can suspend that right - BUT she's getting a real treat in having you show up to pick her up. She's defiant in class, so I'm not sure how it helps to have her not only beat the teacher at her game but also you and your husband at yours!
So she probably needs to be MUCH more inconvenienced. I would take the approach - and admittedly I'm at a distance and with limited info - that roaming around and not sitting on the rug or lining up or whatever are what TODDLERS do. They are too little to behave, they don't understand the rules. Okay, if your daughter is too little for rules and kindergarten, then she is also too little for: (fill in the blanks as you wish) screen time, TV, toys suitable for 5 and 6 year olds, unsupervised use of markers and glue, alone time in the yard, shopping trips, play dates, movies/TV for kids her age, etc. She has to be absolutely miserable and treated like a baby - and tell her that, when she's older and more mature, she can have big kid toys and privileges. She can have baby coloring books and nap time and early bedtime and so on - but with as little interaction on a "big kid" level as you can manage. So NO she isn't going to the XYZ movie and she isn't having a friend over because you can't supervise her constantly and you can't trust her alone because she doesn't follow rules, and NO she isn't getting toys with the recommended age range of 4 and up because she's in the 2-3 range. Let her be good and bored with toddler toys and absolutely no electronics.
I wouldn't use too much "Santa won't come" unless you are absolutely prepared to make Christmas a battle ground. But I do think you can cross certain things off her list.
I'll add the caveat that if she is suffering from something like oppositional defiance disorder, then she needs intervention. She may need therapy anyway - and the whole family can benefit from learning effective techniques.