I definitely think my rabbits can sense my emotions. If I come home from work and go out to the barn upset or uptight, the rabbits are all on alert, watching me, trying to figure out what the "threat" is. If I walk out there in a good mood, they usually won't even get up for me... (Well, until I open the feed bin! LOL!) And of course, there is no way I can stay stressed or upset for very long around my rabbits... nothing calms me down faster than taking care of my rabbits!
When I'm at a show, if I get uptight or stressed, I find my rabbits are stressed too. They are more squirmy and tense. But if I am calm, they are calm and easier to handle. And it doesn't matter how fast I'm picking up and putting down the rabbits, just how stressed/tense/uptight I am. Give yourself time to "learn" your bunnies, and give them time to "learn" you. Trust is a huge issue with rabbits... give them time to trust you.