I have generalized anxiety and one of my big things is getting trapped in traffic, at lights, traffic jams, heavy traffic, etc...so I really had to work on this.
I know you can do this. You need to go online now and get a map. Look at the streets to the horse show in detail. Find a route that you are comfortable with, not the big 4 lane highways unless there aren't any other roads but take a look at them and see if there is a smaller state highway that would be more comfortable for you.
When I went to collate at OSU in Stillwater Ok I would drive down 177 towards Perkins OK but take highway highway 33 to Guthrie OK where I would get on I-35 until I got to north OKC. It was a nice pleasant drive with very little interstate driving. If I took 51 to I-35 it was flat and boring and 4 lane divided highway all the way. Then I was on I-35 for almost an hour into OKC and it was almost always heavy traffic once you go to Guthrie.
So I took an alternate route that "I" was comfortable with.
Your hubby needs to understand you don't need to do this cold turkey. You need to plan this out, mentally be ready, and do it your way. I drive early early in the morning or super late at night, like after midnight, when I do long drives and I never do it without an adult awake in the car with me. Just my preference.
You will do fine, just take a look at the maps, plan where you can pull off if you get frustrated or flustered. Look for convenience stores, small roads, little towns, any place where you can count off the miles until the next easy place to pull off. This will give you an escape route, it will make a huge difference.
When we drove to Billings Montana I had a stop that "I" could go to about every 12-15 miles. I would tell myself if I had a panic attack I only had to stay on the road 4-5 minutes and I could have a safe place to pull over then.
Planning this trip in advance and having all sorts of places planned where you can get off the road safely is going to make a huge huge difference.