The ironic mother
Instead of positioning herself as a resource for Precious like mothers typically do, Mary considers her own daughter competition because (brace yourself) she is jealous that her husband would rather rape Precious than her. For this reason, Mary begins to treat Precious as an outlet for all her negative emotion. When she gets mad, she often beats Precious, even when Precious has nothing to do with her emotion.
The ironic father
A father's role in the home is to assist in the creation of babies, but he's supposed to do that with his wife, not with his first-born daughter. This man is not only a pedophile and a rapist, but also, when Precious becomes overweight, he doesn't stop raping her. For him, this has become about exerting power over her, dominating her emotionally and spiritually by keeping her in a state of paralysis, confusion, shame, and loneliness.
There are many aspects about this character that are ironic, but suffice it to say that he should be showing her a way forward in life, not intentionally holding her back. Also, the pedophilic incest is ironic, since it's undeniably evil and perverse.
The irony of Precious's social mistreatment
Part of the damage her parents inflicted on her is Precious's social phobias which often keep her from participating fully. This makes her an easy target for bullies. They bully her for her weight problem, her race, her perceived stupidity (she has emotional problems that prevent her from reading and writing). This is ironic, because it's the last thing Precious needs, and if anyone took the time to just ask her about her life, they might have been able to save her from her fate by reporting her parents.
The irony of Precious's children
Precious's children are symbols for irony because their father is an ironic person to be their father. Precious's own father raped her for the creation of these two kids, meaning that they aren't just Precious's children—they're her siblings too.
The poetic hero
In the end, Precious finds her voice, just in time to deal with the heartbreaking news about her own infection with HIV (by the person who gave her life, which is situational irony). But not only this, she also achieves a heroism through her voice, learning to write poetry, and learning that when she puts herself out there, people actually really like her, contrary to what she was taught to think about herself. In a brilliant irony, Precious succeeds in exactly the most unlikely way, changing from remedial non-reader into a wonderful poet.
