It's not grammatically correct (Rhonda's right) to hyphenate -ly words. Usually. There are a few instances. But in this case, happily ever after isn't being used to modify anything. Sharp-dressed man, for example, is hyphenated because sharp-dressed, as a whole, modifies man.
In my example for happily ever after, though, it's not being used as a modifier. It's being used as a noun. "I'm searching for my happily ever after." Or "It's all about the happily ever after." The person isn't searching for her happily, her ever, or her after. She's searching for them as a whole (if that makes sense). That's why I'm confused!
Thanks for all your responses, though. Grammar is so much fun (and no, I'm not being facetious).