Molly Weasley’s second cousin is not a wizard but an accountant. This mundane profession is enough to embarrass the rest of the family; Ron says that they never talk about him (PS6).
In early drafts of book four, this second cousin was the father of Mafalda, a rude Slytherin girl. Rowling discusses the accountant cousin on her website, referring to him as a stockbroker who married a Muggle. She writes that he was very rude to the Weasleys. When he discovered that his daughter was a witch, he sent her to live at the Burrow for the summer after her first year at Hogwarts. This part of the story was eventually dropped (JKR).