Another Man's Poison (1951).

Gary Merrill and Bette Davis
in Another Man's Poison

In Another Man's Poison, Bette Davis is a mystery writer juggling an inconvenient husband, a lover, a blackmailer (Davis's then-husband, Gary Merrill), and a nosy veterinarian (Emlyn Williams). The film, produced by Douglas Fairbanks Jr., is based on the play "Deadlock" by Leslie Sands, with a screenplay by Val Guest.