I think you'll be good on rainy day.
Limited coverage, unless comfortable in rain
Most of the park is outside. Probably less people but not sure if they will be doing their shows. You could call and ask about how they do the shows on rainy days.
I wouldn't recommend going in a downpour. They do have shelter areas, but for the most part it's an open area with a swamp at the end of the trail.
We went on a somewhat rainy day and it was nice. They have some cover but not a lot. Just bring a poncho and you should be good.
Thanks! Your answer is awaiting moderation.