Oliver veers into this. While he is controlling and demeaning, and just as pig headed as Barbara, he maintains some degree of love and empathy for her, while Barbara, even in an early state, maintains a sociopathic and vindictive disinterest in anything but maintaining her house and image, and will genuinely commit any atrocity to get rid of Oliver, if not take his livelihood with it. That obvious reasons insist that he is pretty much always on the losing end against Barbara only exacerbate this.
The line was in fact drawn during the climax. Originally Barbara was to have genuinely killed and served Oliver his dog out of spite, leading Oliver to snap but still be comically overpowered. Test audiences found this scene unsettlingly callous, leading Barbara to be rewritten as bluffing and adding a shot of the dog outside alive and well.