I'd move, it benefited me when I did and I was also able to try out a few awesome trainers and get a taste for some different teaching styles so go for it if you think it would help your riding in the long run
Honestly I've been through the same experience, the care wasn't great and the best trainer I've ever had left the barn due to that. We started searching around and eventually moved to an amazing barn. If I were you I would just look around, see your options, and look at how it might change when you move. It doesn't have to be a decision that's made right away. But choose what's better for you and your horse. Not for the people around you.
I'd look at it from my horses happiness/healthiness point of view. If the care is better in the new yard and would improve my horses daily life I would probably move. Consider turnout facilities, how often they are mucked out and fed etc.
Also if the training is better I would move too. I moved from my old yard and it was the best decision I made because my riding has improved so much, I've made new friends and kept in contact with my old ones too!