I’ve unfortunately had some terrible experiences with my local vet clinic and I very nearly swore off using them. There’s one vet I do trust for certain things but I am not certain I would go to them in an emergency rather than haul somewhere else. They have multiple vets at the practice and like you I had multiple mistakes.
They took dental x rays incorrectly so they had to be retaken by the dentist.
They did the dental on my old mare incorrectly and that also had to be redone a second time a month later by a different practice.
The emergency vet nearly put my mare down for colic and said there was nothing she could do. I called the nearest vet hospital, spoke to their vet on the phone, and they did not feel like we were at a point that we needed to euthanize. Transported my mare who was in excruciating pain (Because the emergency vet didn’t give anything for pain relief other than banamine). My mare survived and didn’t need surgery. The bill from the emergency vet was $800 (for doing absolutely nothing useful in my opinion).
If anything major happens going forward, I’m hauling straight to the equine hospital. There’s more you can do for pain relief then just banamine and it doesn’t take a genius to run some fluids.
In an emergency, you are at the mercy of whoever happens to be on call. Perhaps you will get a good vet, and perhaps you won’t. I would not completely cut ties with your current vet practice. As far as they need to know, they are still your vet.
I have tried calling multiple vets during an emergency and most won’t even call you back. I did reach one vet who was snippy with me and said, well you didn’t pull coggins with my practice so I don’t need to see you for emergencies. (My horses weren’t due for coggins for 9 months when she was last up, so why would I pull new coggins?).
Most vets in my area will not take anyone in an emergency if you are not an established patient. Which really is bad for the owners because in an emergency you can’t always get a hold of anyone.
The safest bet is to be established with 2 practices and even then it’s not a guarantee they will be available if you need them. An equine hospital is expensive but at least they are available when you need them and you don’t need to call and wait and wait for a possible call back that may or may not come.