I think you can restore order with a collection of "soft skill" tactics. Show, don't tell, and lead by example, and do so quite deliberately, i.e. this is not about being nice and hoping she does too. I'll call her Bev.
Sometimes she will rush me to finish what I'm saying at a meeting
Do not let her take the floor from you. Try things like:
- "Continuing from where I left off..."
- "I agree with Bev, and as I was saying."
- "Thanks Bev let me get to that." ("Thanks" really means "Excuse me" but is more collaborative.)
she thinks we are having too many meetings and taking too long
And I'm sure her opinion of the length of quantity of the meetings is not on topic for the meeting she is presently in, so restore to the topic of hand. If you are feeling sarcastic perhaps smile and mention remarks like that is the reason why we take so long sometimes. Conclude the meeting with a nod to her good intent: "I'll send out an agenda next time and anyone who thinks we can resolve things offline can let me know."
Or maybe she does not need to attend these meetings. You would want to figure that out with her.
"I don't think you understood" when we have different recollections on a certain issue from a previous meeting
Does it matter? "Regardless, I do not think that is the best way to move forward now. Can you explain to me why it's not without quoting the meeting?" Or, "Please correct my understanding then, I am listening."
You should catch these condescension moments and hold her accountable. If my subordinate tells me I didn't understand something, I generally expect them to be ready to elucidate me. They usually are. If not, they are embarrassed, and I do not embarrass them further and we move on.
I have never seen her talk to other employees or our outside vendors this way, so I can't justify why she would do so to me.
For a lot of reasons, actually. She is terrified you may hold her to higher standards and fire her. She is (misguidedly) trying to show off. Perhaps to win a promotion. Perhaps she feels competitive if you are both women, or perhaps she has double to prove if she is a woman and you are not. Honestly this should be somewhat assuring to you - clearly you have someone capable of respect who is running into difficulty sharing this with you.
My priority would be to turn her microaggressions into opportunities to hold her accountable in respect. She probably feels in some way unsafe with you (being dumb, making mistakes, being wrong, etc.), so you will want to demonstrate your respect to her overtly as well. For instance, if she thinks you are wrong, this is a great time to both hold her accountable to articulate why and genuinely be concerned and curious she has insight you don't right now (which is probably true).
Note to people who prefer answers stay gender neutral unless there's a "smoking gun" that sexual harassment or discrimination is involved: I've heard plenty of women and a few men, and have had the fortune of going through HR trainings explaining how gender "dynamics" show up in situations like this, usually in the form of discrimination, or fear of discrimination (plausible here). Obviously none of my answer assumes the woman employee is in the right here. I do go so far as to suggest that the gender dynamic ought to be thought through when assessing how to move forward. The point of posting on workplace.SE is to get advice on topics that you can't just bring up with people in the workplace. Gender is not a large part of my answer but I'm not exactly censoring it to stay politically correct either.