The Baby Diaries: Memories, Milestones and Misadventures is currently lagging behind at 300 in online retailer Amazon's chart of bestselling books.
Daly was due to go on the promotional trail to publicise the volume last month, but ended up scrapping a number of TV dates due to the embarrassment of Kay's behaviour.
A publishing source told the Daily Mail: "The success of books by celebrities hinges on high-profile appearances and energetic promotion. Tess simply felt unable to promote her book in the way she would have liked.
"It didn't help that the revelations about Vernon's behaviour were such bad timing, because the book is so family orientated."
The insider added: "Sales may pick up in the run-up to Mothering Sunday, but any hopes of Tess's book making the bestsellers lists have been dashed."
Kay was last month forced to admit that he had sent racy text messages to five different women. The father-of-two later made a public apology for his "foolish decisions".