it's more common than you think owners taking pets off or adjusting doses of meds.
it sounds as though you need to have a chat with your wife and your vet about this cat in question. as suggested above the Cat's Protection League is someone you could ring to take on this cat if you feel you are unable to look after it with it's medical problems. But be aware if you remove one from the house the other will start to act out as well. so you may have another 'ONE' that you have to deal with. 12 yrs old isn't that old for the average cat BUT a cat with an illness may actually be physically older than they are, if that makes sense. you taking them off their meds may actually exacerbate the situation these meds are generally given and need at least 3 wks to even start to take effect. some cats respond and some need surgery to remove the thyroid. some don't make it at all and get worse and worse. but usually they turn round with the right dose. it's possible your vet has put them on a dose they may or may not need to be adjusted for this cat.
unfortunately you have long haired cats and hair my friend just as having a long haired partner comes with the territory! Dyson makes a great pet hair vacuum and combing your kitties with a nice brush will help.
as for the pooping outside the box, i'm not sure if you mean missing the box or actually pooping away from the box somewhere in the house. so i can't really advise you on that until i know. either way it's a sign something needs to change and soon.