OK's American editor Sarah Ivens said: "My biggest fear is that Larry and Howard may have tricked us all."
"It breaks my heart that OK! has to pull out of a shoot that would have chronicled the next great chapter of Dannielynn's life.
Howard K Stern lost a paternity battle with Birkhead over Anna Nicole's daughter
She continued: "That sort of celebration is what the magazine enjoys most. But first and foremost, we - and I - care dearly about the well-being of the young one, and my moral obligation lies with her."
A new book on Anna Nicole titled Blonde Ambition is reportedly due to expose shock new allegations about the pair, claiming they were somehow working together.
Legal wrangling continues over the estate of Smith's late husband, Texas oil tycoon J. Howard Marshall II, who died in 1995.
It remains unclear how much, if any, of Marshall's multi-million-dollar fortune Dannielynn might inherit and whether her guardian would have access to the money.