If there's no consistent reproducible tenderness, they go home and are told to go to the kid's hospital if the pain gets worse. nausea, vomiting, diarrhea I don't care about, nor do I care about abdominal pain. all I care about is abdominal tenderness. It's either there or it isn't. If it's there and consistent, I send them to the local peds hospital so they can get an u/s by an experienced technician. My tech's are absolutely fantastic where I work, but unless you are well-trained in appy exams and do them regularly, one's ability to successfully find the appendix is very low.
That said, that applies to appy's. Intussusception I always hate. If I'm very concerned I send them to the local peds ED, but if the kid who's having colicky pains every half hour comes into my ER with a normal belly, negative guaiac, and sits there for 3 hours without crying once with mom in the room, they're probably going home.