The man's side of it!

I have four children living at home, all teenagers except for Linda who is a mom. I have made a dish washing schedule for them where each kid gets two days of dishes and Linda gets one. On their dish night, they set, clear and wash the dishes and when the dishwasher is done they must empty it and put the dishes away. Billy's dish night was yesterday and he hadn't gotten around to emptying it yet.
Tonight at dinner Heidi finished first, then declared to Billy, Hurry up and empty the dishwasher. Normally this wouldn't be too big a deal except,
1. Billy wasn't done eating and
2. Heidi screamed it at him at the top of her voice.
Cassie and I tried to explain to her that Billy was still eating and she would just have to wait for him to finish, at which point Heidi went psycho on us. She was screaming at the top of her lungs, "He's not eating, he's just chewing on bones!" She just wouldn't listen to reason nor would she just drop it. She screamed out, " I'll unload it myself and Billy can unload it for me tomorrow!" Cassie and I said at the same time, " No! You are going to unload it not Billy!" More screaming ensued. Cassie got up and started to leave and whispered to me, "Don't help her clear the table." Normally Cassie and I help the kids clear the table and put the food away, not tonight! Billy was completely flabbergasted about the whole episode. He couldn't understand what the big deal was. How he remains so calm when Heidi goes nuts is a mystery. I think he enjoys it! Sometimes he even eggs her on!
Heidi goes off into these fits of rage often, and most often at dinner. It's extremely difficult to not slap some sense into her sometimes. I think even Cassie was tempted this time. Being Heidi's stepfather I often don't discipline the kids the way I think I should because I don't want a conflict with my wife. What can we do when she is so irrational?