Just because someone is older or more educated that doesn't mean they will be right, or know better that someone younger with less education. She probably sees things that way.
Also sometimes people that seem very stubborn is because have a hard time explaining themselves. So you could try helping her to get her point across. Asking her questions and stuff. Sometimes you don't tell someone they are wrong, just make smart questions that will make her see she is wrong.
I don't know on what context these arguments occur, but if she is obviously wrong someone should be able to prove it. In that case I would show her why she is wrong and challenge her to disprove it.
There can not be a healthy discussion if one side is always ignoring what the other side is saying.
If she doesn't ignore what other people say, she will realize she is wrong.
After that if she gets mad, well, that is her problem. It is just part of life and she will have to learn to deal with it.
However if you try to empathize with her, don't use words like "but". Such as "I can see where you are coming from, but..." because that is antagonizing, and is cancelling your first sentence of empathy. This is a very hard thing to do, but it is important for when you have situations like this.
Finally once she has been proven wrong, just ignore her unless she has something to offer. Again, I don't know what the context is, but you could have a moderator validating any new "entry" to that topic. Or if she wants to say something she has to limit herself to answer the latest argument against her position. If she can't, move to the next topic or aspect of the topic, but act like nothing happened, ask for her opinion, that way she will feel it is not something terrible to be wrong, and she can move on also.
Don't stay on a topic forever if there are new ideas worth saying. If a topic is dragging a long time, you can set time aside for later discussion when people has cooled off and in the meantime continue with the next topic.
If it seems not possible to get to an agreement, agree to disagree. Sometimes is just not possible to have everyone in agreement. If you gave her sound proof that she is wrong. And she insists and you don't want to continue, agree to disagree.
If she is being disrespectful, ask politely to keep the talk civilized but direct the request to everyone.
Eventually she will learn, or she will leave.
She may be upsetting the group, but it is better if the group learns how to deal with this kind of things.
You can't shun away everyone that upsets you. Take it as a learning opportunity on conflict management.