Cat won't poop in the litter box!!!

I have a 2 year old cat and I introduced a 7 month old kitten into my house a month ago. He was sick when I got him so he stayed in one room, he had cochcidia and had diarehia. Once he got better and used his litter box, we introduced the cats, they seem ok, fight and play but don't kill each other. The problem I am having is that the baby doesn't go poop in the litter box but instead goes in the Florida room. I don't know what to do, I can't catch him in the act, he goes while I am at work. Does anyone have any suggestions? I believe it is behavioral, he goes pee in his box, just not poop. I need to figure out a way to train him. I really can't afford more vet visits. Please HELP!!!!

Do you have more than one litter box? Can you put one in the Florida room? Uncovered poop is a dominance thing. When I first brought a second cat into the house (I did get a second box) they had a battle of the boxes for a while.

Thanks for replying. I do have two covered litter boxes, one in each bathroom, I made sure to get another when I got the 2nd cat. My 2 year old (Binks) uses the 7 month olds (Chester) and his own. Chester uses the new one. I could put a litter box in the Florida room, but I don't want one there permanently, am afraid he will train to only want it there. Could Binks be bullying Chester, he does seem to like to stand right outside the box while Chester goes to the bathroom and rush in there once Chester is done! I try to tell Binks no, and move him away from the box while Chester is in there, is that the right thing to do? I have never had two cats before or lived with two cats before.