Oh gosh, I've always heard that three is like a teenager! Hugs, mama. On the other hand, I've heard that four is MUCH better, so hang in there. I think church and restaurants might still be a bit too much at this age.
Well, I'm kinda shooting from the hip here, but maybe sit down and try to figure out what's going through her head. She's in a new situation. It's probably stressful to go from having one-on-one adult contact to being in a group of kids. She may be just as upset about not knowing how to act as you are about her not knowing, kwim? Maybe you could try some roleplaying stuff with her when you're home together. Put her dolls or stuffed animals through scenarios similar to problems that she's having. Like, "Dolly was playing with this car, and then Teddy came over and hit her and took it away! That wasn't nice of Teddy. See how sad Dolly is now?" etc. I think it's such a slow process to instill empathy and respect, and it's easy to get frustrated when it doesn't happen fast enough. I know it starts with modelling empathy and respect towards the child and others around us, but I think there's a lot of explaining and working with and maybe just waiting for it to click. Anyway, I hope that helps, I'm a little rambly today. ;)