I [30M] am still friends with an ex from high school/college. GF [30F] thinks its weird and wants me to break the friendship

We've been dating for about a year and have talked about getting married. We had discussed our past relationships and I talked about an ex from HS/College that I chased for all of my college years. We both did stupid immature things to each other during that time but shortly after graduation we sat down, apologized to each other, and we've been good friends ever since.

Flash forward to now and this ex has a husband and kids so we don't really hang out too often. Early on in my relationship with my current GF I went out to a couple of things with the ex and though my GF said it was weird she didn't say much else.

This weekend I went out with the GF and some of her friends for dinner and drinks. I got a text from the ex saying that a mutual friend who I hadn't seen in several years was in town and they both wanted to meet my GF. I told them about the dinner and drinks, and they said they could meet up for drinks. My friends drive 30 mins to meet up and my GF is incredibly rude to them to the point where my friends leave after about 15 minutes.

Now we've been fighting over this for over 24 hrs, with her friends telling her shes right and my friends telling me I'm right so I'm asking impartial internet strangers what they think.

Her points:

* It was rude to invite people to something without checking with her (though she later admitted that it was just the invitation of the ex that bothered her) * It's weird that I'm still friends with an ex * In choosing a friendship over her feelings, I am devaluing my relationship with her for a friend I see only a few times a year.

My points:

* It sets a bad precedence that she can pick and choose who I hang out with, especially one where the friend has done absolutely nothing to her * The amount of time I hang out with a friend does not always correlate to how much I enjoy their friendship. I don't hang out with any friends often anymore because life happens, that doesn't mean I don't value each and every one of those friendships * This isn't the type of request people in stable relationships ask of each other. This is like saying "If you really love me you'll rob that bank"

She claims that she's not worried that anything is going to happen between me and the ex, but at the same time she seems to think that I'm not over the ex.

tldr; Am I being unreasonable because I won't throw away a friendship with someone I dated 10+ years ago?

EDIT: I'm referring to my ex as "the ex" in this post for the sake of clarity but IRL I refer to her as my friend only. When I first told my girlfriend about the past relationship I left names out, but she figured out who the person was by looking through old facebook posts.