In the future, if you have 3 cats, you'll need 4 litter boxes. Really.
However, once they poop/pee outside the box, it's over. Repeat- it's over!!! They'll continue to do so until they die. There is no way to get odor out of the carpet unless you replace the carpet. Those enzyme products (Super Anti-Icky Poo) work fine, but if you miss treating even one molecule of urine, the smell comes back. And Super Anti-Icky Poo is expensive!
If there's a veterinary problem,the only way to figure that out is to get a bunch of expensive tests, so use your judgement. But most of the time, it's just the way cats are!
You have 3 choices: 1- Kennel the cat all the time, 2) Let the offending cat live outside. Even declawed cats tend to do ok. I've had 2 cats that lived to be over 17 years old living outside--they were declawed; 3) put the cat to sleep.
If you don't do one of the above, you and hubby will just end up hating and resenting your cats even more (yelling and rubbing their noses in it actually makes matters worse), so take stock of your emotions and figure out how you want to handle this.
Sorry- not the news you wanted to hear, but that's the sad truth about cats and vets won't tell you this.