Hi, V.. Well, it sounds like you really do know your son very well in terms of your instincts that something is bothering him about pooping in the potty, and that may be what's holding him back from pooping there.
The fact that he hides, I think, is a really good clue. Maybe he's ashamed of his poop. Maybe because it smells bad, and he knows it's dirty, he doesn't want to do it there. He wants to do it in secret. I know that makes no logical sense because then he comes to you for changing, but 3-year-old logic is very, very different from adult logic.
Maybe if he sat alone on the potty and you were just in the next room where you can hear him if he needs your help, maybe that would give him a sense of privacy and such. Maybe for him it feels more dignified to do the pooping process in private, and then get your help with the aftermath. Try giving him a compromise that will give him a little more dignity than having Mom watch him. He doesn't have the words to tell you this, but his actions are his language. He doesn't want to go in front of you.
Also, even though you are being every bit as patient and nice as humanly possible, you do have negative feelings about this whole snag in the pooping process, and I'm sure he's picking up on it. Maybe if he didn't have to feel your anxiety about the fact that he hasn't mastered potty pooping yet, he might do it all by himself.
Also, I think that maybe he might be hangingin onto this last little bit of babyhood by having you clean up his poop. He wants to be a big, big boy, but he still needs a little reassurance that he's not going to lose that attention and protection.
#1 - make him help you clean up his poop from the diaper or his pants. Do it together as a team. I'm sure he won't like that, and he won't be very good at it, but get him to wipe his bottom, scrape out his underwear or something, gently make him participate in the process of cleaning himself up, and then gently let him know that if he poops in the potty, he won't have to do this cleaning up of his pants anymore. The potty takes it all away, just like his pee, and no one has to deal with it. That's a good, gentle deterrent, a reason to do things differently in order to avoid something unpleasant. It's just an idea. See if it helps.
#2 - Make sure you give him plenty of attention in other ways. Make sure he knows that you will always love him and that will never change. Even though he goes off and does things on his own, seek him out sometimes and let him know you'd like his company, that you'd like to play with him, and he won't need to get your attention when his independence wears out and he needs some little guy reassurance. This can help bridge him into letting go of this baby behavior of needing to be changed like a small infant. Also, see if you can show him a baby in a poopy diaper being changed; let him see that that's something just for babies, and he's a lot bigger now. Let him see the comparison between himself and the tiny baby.
#3 - You can try a little amateur art therapy with him. Sit down and draw pictures with him for a while, and then maybe the two of you can each draw the potties you use. See if you can get him to draw what he likes about the potty, and then have him draw what he doesn't like about the potty. He may surprise you with his artistic answer. He may give you a clue about what's bothering him, and you might be able to clear up some little fear he has, or take away some discomfort he might have.
See if Dad can help with the process, too. Maybe Dad can talk to him, without any pressure, about what it feels like to be a big boy and poop in the potty. I don't know how open your family is, but maybe if Dad can let the little one see him do it once (I know that sounds disgusting, but it sounds like you're desperate to have this resolved). Maybe your older son, if he agrees to help, can talk to the little one about it, too, how nice it is to go in the potty, so the little one can be a really big boy, too. It's just a suggestion. Don't do anything your family isn't comfortable with.
Anyway, I hope my suggestions are helpful, and I hope that your family gets through this without any further snags in the process.
Peace,
Syl