4 year old won't poop in the potty

I have a son about to be 4 years old. He has been peeing in the potty no problem for the past 9 months. However he refuses to poop on the potty. I have tried sticker charts, praise, toy incentives, I've explained to him about how big boys use the potty and how his friends use the potty too. But he gets upset and refuses to poop on the potty. He was constipated once before which I think regressed him even more. He would rather go in his pull up outside and hide but even to do that I have to coax him into "letting his poop out." Sometimes he just holds it for a couple days thinking the poop will just magically go away.
Not sure what to do next? Starting to get frustrated and just want him to see how easy it is to poop on the potty. He seems to be not interested in being a big boy and says he is a "baby." I do have a 1 and a half year old daughter which might have something to do with that??
Any suggestions would be greatly appreciated!!!!!! This potty training thing is wearing me out!!!