The ideal way to do it is one show cage for each of the two males. If I want to put three together, I use one show cage apiece for two of them, let one run around, then rotate the the two out and put one in a cage. After 3 or 4 days of that, I would probably try letting the little one out with one of the other males, while keeping the second male in a show cage. Then switch again so the little one is out all the time with one or the other of the larger males. I would also be sure to whack the whiskers way back on the two older males to try and keep the dominance to a minimum.
In a situation like you are describing, I would expect it to take at least a few weeks before I would be comfortable letting them go together. It's been my experience that trying to add a same sex "third wheel" to an already bonded pair doesn't work well. Adding a male to 2 females is one thing, but it would be pretty tough adding a female to two bonded females or a male to 2 bonded males. Be VERY wary of doing this and be VERY sure to be attentive to every little thing. That little boy will have zero chance if the other two turn on him.
Honestly, if it was me, (and I read this situation right) I would get the little guy castrated and leave him with mom. It could save you a ton of heartache down the road.
Also, a cat carrier isn't going to achieve the same result as a show cage. The entire purpose to the show cage is so that they can see, sniff, and interact with each other. A cat carrier is going to have a whole lot of plastic between them. I also wouldn't introduce them with the two in one cage. If they decide to turn on each other, and they very well might do that, then that is an incredibly small space with no way for one to get away from the other. I would invest in a couple show cages and use those instead.