So if you sit down at night to watch a program that you've been wanting to see all week long buuuuut it gets interrupted not once, not twice, not even three times, but a toal of 8 or 9 times by the cat jumping on the table and pulling & chewing on the blinds to the point where it has to be paused that many times to get him to stop - WHAT would be your reaction finally(happy or angry)??
Then to top it off your spouse tells you that you're not allowed to yell at him and not allowed to put him in another room to make him stop, and the show finally gets ruined because of it!
Obviously your wife's idea of what is cruel is pretty bizarre. I'd tell her to find three experts who say that it's cruel to put a cat in a 10'x10' room for an hour if she wants me to abide by her definition of cruel, or to get your vet's agreement that this response is cruel. But in any case, this is NOT about cruelty to the cat. It's about the two of you are both on a warpath to destroy the other and prove yourselves superior.
When it's more about being "right" than about finding win-win solutions to problems, then your relationship gets into serious trouble.
For your part, I can see that you're probably sarcastic and belittling toward her. Stop that 100% no matter how frustrated you get if you want your relationship to survive. Instead, have a calm discussion where you tell your wife that you want her to feel good about the way you care for her and the animals, and tell her that it's not fair to expect the cats to decide how your household operates. Therefore, if she will not let you put them into a room temporarily, you'll accept any solution she provides as long as it solves the problem at least 80% of the time, but that if she cannot find that solution within a certain amount of time, then you will conclude she's unable to fix the problem and so you will.