"They express their happiness."
Translation:Ellos expresan su alegría.
Both should be correct. There is a small difference between Alegría and Felicidad, though. Alegría refers to the emotion that makes you smile, while felicidad is a deeper kind of happiness.
So are you saying alegría indicates mild happiness and felicidad indicates great happiness?
sort of, but also, alegría tends to be a short-lived feeling, while felicidad is supposed to be a deeper, longer lasting state of being