The irony of shame
The ironic part of Josie's shame is that she has done nothing wrong. She is not responsible for her mother, or her mother's decisions, but still, she feels plagued by them, as if they are a reflection of her. There is another related irony that is more subtle: Josie doesn't even hate her mom for prostitution. She hates her because she's a bad mom. The issue of prostitution just shows one concrete example of that shame, but when Josie assumes her mother was involved in a local murder, the reader can see that the shame is even deeper than the issue of sex work.
Name, identity, and family
Josie's name itself is ironic, because (just as surnames sometimes reference the family profession) Josie's name signifies her mother's profession: prostitution. In Josie's world, "Josie" is slang for prostitute. So she is constantly haunted by the reminder that her mother is a prostitute, because the reminder is literally built into Josie's name.
The irony of hope
The irony of hope is that although Josie works hard, she still ends up coming up short when she goes to pay for college. It would seem that prostitution is the hopeful answer, since it would give her the money she needs to make her dreams happen, but actually, her hope comes in the rejection of easy money, and her commitment to follow her conscience, something her mother does not do.
The Anti-Mother
Instead of having a mother that represents life, growth, support, and potential, Josie's mother represents the opposite of all those things. Josie's mom is extremely self-interested, ruining Josie's life in a variety of ways. Not to mention that Josie suspects her mother's evil goes way beyond what she has personally witnessed. She notices when a rich man turns up murdered, and she can't help but assume her mother was involved. That's a pretty dark assumption to make about one's own mother, but then again, she might have a point. The mother is ironically opposed to Josie's well-being, instead of being a supportive mom.
The irony of Josie's fate
In the end, Josie picks exactly what the reader would suspect. She chooses not to be a prostitute. But that doesn't mean there is no irony—first it's ironic for her mother to pressure her into prostitution. Secondly, it's ironic that with so many emotional grudges toward the industry, that Josie feels tempted by the offer to make money sleeping with strangers. She chooses correctly for her purposes, but that close encounter will definitely shape Josie's life.
