Hi M.,
I want to offer words of encouragement! My husband and I successfully potty-trained two boys (now 2 and 4) before the age of three. 3 is a tough age, because little ones want to try breaking every rule you set for them, and sometimes the wierdest things become a battle (oy!)
My first was the most like yours, not wanting to poop in the toilet. I did not try reward; or poopy-dances; or talking or punishing. I read one article from a man who teaches/encourages old-fashioned parenting. He had a simple suggestion that took a little time and effort (and dedication) on my part, and it *worked.*
At my son's normal poo-times (immediately after breakfast and before his morning nap (after lunch), I'd sit him on the toddler potty-chair, I told him to not get up until there was a poop, then I'd leave the bathroom and close the door.
Walk away.
Oh yea, he cried for 45 minutes the first day! -- but he made a poop.
The second day he cried for 30 minutes. -- but he made a poop.
The third, fourth, fifth, and sixth days, he cried for 10 minutes.
The seventh day, he didn't cry at all, and left me a poop in 10 minutes.
But we kept up the routine for another month just to make sure.
Good luck!
t