First off, if she's caring for an Alzheimer's patient, cut her a lot of slack. Tons. Tons of tons. And keep in mind she may be getting demented herself, especially with a personality change like that.
Have you tried confining your rooster at night? Building a box or bringing him inside, keeping him someplace dark?
If everything else fails, I gotta agree to let them go. If they're illegal, they're illegal, and you knew that when you got them. I understand it sucks, but folks that live in the city limits live there for a reason, they want a city type life. If they move to the country, all bets are off, imo, but if you're in their territory, you've got to play by their rules.
Also, you don't know what's going on inside that house. Depending on his level of disease, could be that rooster's crowing wakes the Mr, and she spends the whole morning trying to convince him he doesn't have to go out and do chores (like he did as a boy)---it may be triggering a lot of stress for them. Or, Mr could be up wandering much of the night, and she doesn't get any sleep. You just don't know.
Does she have family you can talk to? Sounds like she's having caregiver meltdown, and that's putting him at risk also.