I think it is frightening her, and for good reason. I would be concerned about the dogs playing chase with your bunny, as that is a natural urge and prey drive for dogs. No matter how harmless it seems, when the rabbit runs and the dog chases, their instincts tend to kick in. The dog is most likely thinking “catch dinner” and the bunny is thinking ” escape or be eaten”. Yuki flattening herself to the floor is probably self defense mechanism- she can’t escape in the enclosed surroundings, so she tries to make herself as invisible as possible.
I don’t mean to sound harsh, it’s just out of concern. There are so many incidents where perfectly sweet, well trained dogs suddenly attack or devour their non-predator companions. You are obviously a caring bunny and dog owner, and I’m sure you would be devastated if anything awful happened. I wouldn’t let the dogs and rabbit together for now. You will probably never be able to leave them unsupervised, so they really don’t need to learn to “get along” beyond the dogs getting using to seeing the bunny without chasing her. Even very small dogs can kill larger rabbits ?.
Sorry to be a downer, and I respect you for asking about this ☺. Getting information is the best way to go about giving our furry family members a wonderful, safe life.