Yes, as someone else put it -- being very consistent with her is key. But you also might be talking about this so much with her -- meaniing to reinforce the lessons -- that it's actually ceasing to have much effect; in other words, she might be hearing your messages about respect, how she's the child and you're the adult, etc., that it is now "going in one ear and out the other" rather than taking root. If she already has the mind-set that she is basically a small adult and the equal of not only her peers but her parents and teachers, she may be tuning out anything you say that goes against that firm belief.
Also, you note that she has not hurt anyone and doesn't want to. But unfortunately her intentions won't matter if she takes another child by the shoulders (as you describe) and shakes her and that child decides she has been hurt; your daughter will end up in the principal's office or at home on suspension. The hands-on habit is the very first thing to deal with because it is very likely to end up with her in possibly serious trouble at school.
She sounds overall like a smart, affectionate kid and that is great. At this point, before she gets older, I would first go to the school counselor -- just you and your husband, not her -- and talk frankly about everything you've said here. I would emphasize to the counselor that you do not think there is any "condition" going on and there are no stresses or changes at home; this is a matter of her basic personality (which is basically loveable) that you want to work on sooner, not later. We're just talking short-term behavioral management here.
Ask the counselor for specific strategies and even short "scripts" to use at home with your child (i.e., when your daughter is acting like she is the adult, how you can deflect that, etc.). Ask for good books about child development and children who are strong-willed and/or defiant. This is why the counselor is there. Then see if the counselor will do a series of meetings with just her and your daughter to talk things through. Of course the counselor shouldn't tell her "Your mom and dad say you are bossy" etc.-- the counselor should know how best to handle these meetings with your daughter and should focus especially on her behavior toward classmates and teachers.
If the school counselor isn't great, or doesn't offer to counsel your daughter for a while to help with this, you might want to check into seeing a family counselor for a short time, one who specializes in younger kids.
A lot of her defiance and "I'm the adult" attitude is pretty normal for a smart older kid (is she the oldest child?) but if she's as lacking respect as you say, and you add in the lack of understanding about personal space -- I would go ahead and get a little help with this to turn things around and make your life with her pleasanter for both her and you, before she hits the "tween" years when her approach will be tougher to change.
One other thing: Give her things to be in charge of! She wants authority, so give her some of her very own whenever you can. Make her responsible for something around the house that matters to her (not just a regular chore but something bigger -- like she's the boss of the Easter dinner and gets to make out the shopping list and arrange the table etc. Surely there are better examples but I can't think of one....Ask the counselor!). Giving her some responsibility and praising her when she handles it could help her feel like she does not have to run everything else.
Post again and let us know what happens. You CAN all work through this.
P.S. Tying her hands behind her back? Someone suggested that. It would backfire and make her more defiant, not less. And she won't have anyone to tie her hands in the heat of the moment at school when she wants to reach out and grab another child's shoulders; she needs to learn self-control, and physically restraining her will not teach her anything about that. She will resent you for it and be even more sure that she, not you, is in the right. And if she mentions at school that her parents "tie her up" you will quickly get a visit from your local authorities. Please don't do it!