E.Z.
Hi
I had a similar problem with my son as well.
He on the other hand would hold it forever, until he would feel comfortable going....in a diaper.
One time we had out of town guests, and he would not poop for 3 days, until finally the guests went out of the house for a few hours and he felt comfortable enough going. (I finally had to tell them that they needed to leave the house so he could do his business) All this was going on when he was about 3 to 3 1/2 years old, and he would pee on the toilet fine, and was wearing regular underwear for the most part of the day. My son would put off pooping, probably because he was disgusted himself, and this made him constipated.
I saw several specialists for this, and he was given Miralax mixed in with his drink once a day.(This is Over The Counter nowadays)
At the time the guests were there, he was on it....so now you can tell what will power will do! I just knew he would do it when he was comfortable doing it.
It honestly took a LOT OF coaching and insisting, bribing and ensuring that this is what everyone does etc.
I even let my son pick out a potty he liked, but he did not actually try to use it (he was peeing fine in the toilet) until his MUCH younger sister (18 months) sat down on it and pooped one day. And Voila! It was like a "If she can do it, so can I" moment.
I also let the potty be in the room they spent the most time, so it was readily available (no running to the bathroom and changing their mind), many naked days, and plenty of luiquids to make them go more often.
It is REALLY hard to go get them to go that first time, but after that it should be ok.
My son is now almost 7, still tries to get out of going to the bathroom since it is such a chore, and sometimes he needs to be reminded. But, every child is different, and there are many ways to deal with this.
Now you know that you are not the only one at least!
Oh, by the way, once my son started going on the potty/toilet we realized he really wanted to be alone when pooping (privacy thing) so that might be something you can try too.
Good Luck!