The standard Italian sentence (low, colloquial register) would be
La macchina è mia e la tengo come [cazzo] mi pare a me, va bene?
The car is mine, and I keep it (how I [fucking] like / how [the fuck] I want), is that fine?
As noted in the comments and in the other answer, cazzo is used as a generic expletive, like fucking in English. It is idiomatic to add it without prepositions after come or other interrogative pronouns, exactly like the fuck is used in English.
Note that another expression that is grammatically incorrect in textbook Italian but common in the low/popular register is mi pare a me: grammar rules would dictate that either mi or a me is used, but not both.
The 'endearing' version cazzuccio is non-standard usage; the author used it as a literary device for comic effect here. He is mixing registers for comic effect: those sentences pair a fake exaggeratedly polite / endearing tone with a couple of very vulgar / impolite expressions to invite her not to bother him. See also cariiisssima madriiisssima earlier, where the same fake polite tone is used. Literally it means my dearest motherest: madrissima is another made-up word, where a superlative ending is added to a noun instead of to an adjective. The supernumerary repeating i's and s's are used to show in writing that these words are spoken out slowly, to add emphasis.
Overall this is a very difficult text to read for a non-native speaker. The author uses literary devices, made-up or uncommon words, expressions from the youth slang and Roman dialect, popular culture references.