The relationship between sarcasm and irony is subtle; sarcasm often makes use of irony, but is characterized by its "biting" nature. The quote from my daughter is ironic and sarcastic; the quote about "caring less" is ironic, and may or may not be sarcastic depending on the context.

Irony here refers to verbal irony, a discrepancy between the literally meaning of a phrase and its intended meaning, such as saying "What a nice day!" when it is raining.

Thus, "I could give a shit" and "I couldn't give a shit" are identical in meaning, as the former is doubtless intended ironically. Similarly for caring less.