Can a relationship work if one person isn't that interested?

A relationship will never work if only one person is interested. That's basically common sense. You can never be her friend if you are still upset that she dances with another guy. The best thing to do is to let her go. Stop hanging out with her all together. It's going to be the toughest thing you've ever done considering this is your first serious girlfriend, but trust me if she isn't in to you now she will never be.