I know this post is old, but it came up in my searches so I'll add my experience in case it helps anyone else. My cat had exactly the same thing - split nose that appeared instantly, with no obvious cause. My vet also did not think it was calicivirus and suggested perhaps it was a burn. Well, I...
My female cat does exactly what you describe outside, and pees normally inside in the litter so I assumed she is spraying outside. Tbh it sounds like the real problem here is your husband
