Graduate Student Co-authorship Etiquette (Dissemination of Student Papers Not For Publication)
I understand why you are a little peeved that she offered to send it to the Dean without checking with you first, but I think you need to swallow your frustration on that point.

Instead, you need to figure out what your goals are.  Right now you are reacting: you are letting your emotions control your reactions.  Instead, you should figure out what end goal you want to achieve.

Do you want to make sure that the paper is in good enough shape, before it is sent to the Dean?  Then negotiate a timeline with your co-authors.  This might mean you both have to give a little: you might have to work extra hard to get your revisions in; and they might have to be willing to delay sending the paper a little bit until you've all had a chance to revise to your satisfaction.  That's a perfectly reasonable request.

Do you want to be listed as first author?  If so, why?  You said the paper is not going to be published.  So why do you care?  If you think your contribution means it is appropriate for you to be first author, and you care about it, then raise the point with your co-author.  But approach it with humility and gentleness.  Remember that we're human; we have a tendency to overestimate our own contribution and underestimate others, so you need to correct for that.  Also, definitely do not ask to be first author as a way of getting revenge; that is petty and beneath you.  Take the high road.

And, take this as a lesson.  Generally, it is best to discuss authorship early in the project, not wait until the very end.  In my collaborations, there is often an understanding from the start about who is the lead on the project; the expectation is that the lead has the overall responsibility and will most likely put in the most work, and in return will likely end up as first author.  These discussions about authorship are often easier to happen earlier than later.

Anyway, bottom line: Figure out what you want to achieve (what you want the end state to look like).  Then, figure out how to ask for that.  Set aside your emotions and your negative reactions to your co-author's initiative in moving things forward without checking with you first, and focus on what end state you want to achieve.  I suspect you might find that you share pretty much the same goals as your co-author, and there's no need to get upset or strain your relations with her.