What is the meaning of 臭石头 (slang)?
I've heard way worse when my mum and dad were arguing hahaha. I'm not sure if it is indeed what i think it is, but if it is, it's kinda cute and not that bad. Here is my guess:

Saying one person is like a rock when arguing is simply comparing that person to a rock, and why a rock you ask? Well, you can't win an argument with a rock, rock don't listen, rock don't change, rock never compromise because "it doesn't move". It's basically saying, "You are so stubborn!!".

Now why the term 臭 infront then? It's because if you just say ”你是一个石头“, it misses some "flavour" (See what i did there haha), your dad is just trying to show your mum who the boss is haha. Here is what I mean by that.

你是一个石头(You are a rock!!), flat, no emotions at all.

你是一个臭石头(You are a stinky rock!!), see how it portrays emotions better by simply adding the word "stinky"? It's just the way it sounds sometimes, as Chinese is a tonal language so the same sentence on paper might not mean the same when spoken

Again, this is my best guess, it could be a stronger word in different dialects.