"Elephant in the room" is an obvious problem that people do not want to talk about. Example: The fact that his brother was still living with his parents was a big elephant in the room at every family gathering.
“Between a rock and a hard place” means “to make a difficult decision between two things that are equally unpleasant”. Example: I’m between a rock and a hard place. If I go with Susie, it’ll be much more expensive and if I go with Julie, Susie won’t.