I dread to think how my parents relationship would be like now if my father hadn't died over twenty years ago and my mother wasn't in a home. He was always short-tempered with her, which used to make me cringe. Mum didn't appear to mind at the time, and as an assertive woman she certainly wasn't brow-beaten by him. When he died, I saw a lot more of my mother as she moved near me. At times I could see why my dad got so cross. I'm very like him, and my mother knew exactly how to wind him and me up. This got worse as her dementia developed.
In your dad's case, just keep chipping away suggesting some of the techniques from the Compassionate Communication thread. I must admit I found using them hard as my mum would keep on returning to her pet themes of stealing neighbours etc however much I tried to distract. My brother used technique he learned when training his dog and would hold out an enticing treat to try and break the cycle, and that often worked. Maybe you could suggest tea and cake or something similar to both of them if things get stuck in a loop.