We can infer that Mrs. Wender trusts David and believes that he means what he says when he tells her that he can keep Sophie's secret about her sixth toe. Of course, this is a potential moment of disaster for the Wender family as they have worked so hard to try and conceal Sophie's deformity from everyone. They know, as David does not fully realise yet, that if this is discovered, then Sophie will be neutered and expelled into the Fringes to live with others that have been similarly treated by society.
We are told much later on in the novel that Mrs. Wender always felt that David somehow understood. Sophie herself tells David this when she rescues him:
"My mother said there was something... something about the way you sometimes seemed to understand her before she spoke."
Thus we can see that Mrs. Wender felt some kind of connection and understanding coming from David, enough to trust him with her daughter's secret.