Mildred covers for Veda (Situational Irony)
Throughout the film, it is astounding just how far Mildred's love for Veda extends, the extent to which she is willing to cover for Veda's misjudgments and forgive Veda's ungratefulness. On each of these occasions, it is ironic that Mildred would subject herself to the abuse of her daughter, and the viewer is meant to feel disappointment that Mildred does not stand up for herself more. The most shocking instance of irony occurs when we realize that, even after Veda has had an affair with her husband and killed him, Mildred is willing to cover for her daughter to prevent her from getting arrested. That after Veda has proven herself to be such a bad seed, Mildred still cares for her and mothers her, is disturbingly ironic.
Dead Body (Dramatic Irony)
When Mildred brings Wally back to the beach house, she (and we, the viewer) know that Monte's dead body is lying next to a coffee table downstairs, but Wally has no idea. During the whole scene, we know a key piece of information that Wally does not, creating an instance of dramatic irony. For all he knows, Mildred is finally interested in him romantically, but we realize soon enough that she is framing him for the murder of Monte.
Kay's Death (Situational Irony)
When Kay falls ill with pneumonia, Mildred is with Beragon. With her children on vacation with Bert, Mildred has a night for herself, going over to Monte's and submitting to his seductive advances. While she is kissing him tenderly in front of the fire at his beach house, Kay is coming down with a fatal case of pneumonia. The contrast between Mildred finally taking some time away from being a devoted mother and doing something for herself and this being the moment in which one of her children dies creates a rather tragically ironic scenario. In many ways, Mildred is the most attentive mother, but when she looks away for a second, she loses her younger daughter. Additionally, Kay is the daughter who required less attention because she is less spoiled and entitled than Veda. In the final moments, Kay needs attention more than anything, but Mildred isn't there to give it to her.
Veda and Monte look down on Mildred's job (Situational Irony)
One of the central maddening ironies of the film is the fact that, even when Mildred's job as a restauranteur is the only thing keeping Veda and Monte afloat financially, they still look down on her for working in the service industry. The only reason that Monte and Veda are able to have the expensive lifestyles they have is because Mildred is working to provide for them, but when pressed to say how they feel about it, they both characterize her profession as lower class and embarrassing.