The ironic innocence of youth
The narrator investigates intimate emotional problems the only way she can, by talking to people about it, and when she learns that her grandmother is sick, she wants a chance to work through her insecurities with her grandmother. Ironically, she is positioned to take something from her grandmother. The grandmother gives her love and then when she is dead, only then, the granddaughter realizes that her grandmother wasn't 'helping her solve her problems.' Ironically, the love was the solution, and ironically, it is only experienced in retrospect.
The irony of identity and community
A person's identity seems like an individual thing, but it's perfectly social. Alone, a person would be like their animal instincts, but in the context of a family, a community, and the public, then a person's identity becomes formed, not as a way of being alone, but as a way of participating in the group in a unique manner. The identity question is well explored in either half of the book, the unnamed narrator's stories and Rosa's stories both.
The irony of happiness
There is a poignant irony in the novel's use of the word Happy in this title. Happiness to the innocent girl at twelve means one thing, but after the reader watches her sometimes painful, usually confused journey for identity and peace, they realize a sad twist. Her innocence is being removed from her, and her new opinion of happiness is much more caustic and reactionary than she originally wanted. Happiness is a riddle, it seems, and the title captures the irony of it.
The irony of spousal abuse
Typically, violent domestic abusers are the victims of childhood abuse, which is plainly ironic by design it seems, because of the irony of the abuse cycle. Then there is the additional irony of the husband's role as protector. Instead of using his intimacy and privacy to cultivate love, using his force to protect that love from external harm, he uses the privacy to trap her, and he uses his force to abuse her, though she is hopeless to defend herself, having been isolated by him.
The irony of music
The theme of music's resilient power is obvious in the stories, especially in the stories about the grandfather's love for Salsa. The music is naturally ironic, because music is basically magic (it gives a person power over another person's emotion through an invisible medium: sound), and also because even though she has never heard the music, her grandfather's presence gives her a kind of ethos to experience the music as "her own." She discovers that the experience of music is something she can cultivate to refine her identity.