3 1/2 Year Old Won't Poop on Potty

My 3 1/2 yo daughter has been peeing on the potty for a year. And during this past year has pooped on the potty when she has felt like it but that those times are few and far between. We have tried EVERYTHING. I think I've read everything out there - talked to her doctore - read every post on Mamasource that has delt with this and I am just at the end of my rope. The latest has been a sticker chart (for the 3rd time) and she got to choose her "prize" if she went 7 times /got 7 stickers and so after 6 WEEKS (not 7 days like we'd hoped) we finally took her to Navy Pier to ride the Merry-go-round. Now she has no interest for another "Prize". The rule has also been that if she won't poop on the potty and only a diaper, then she has to poopy in the bathroom. Last night she fought it tooth and nail and through a tantrum because she didn't want to poopy in the bathroom - even though it would still be in her diaper. I feel like every time we make headway she does it once and then bucks the system. HELP - has anyone else dealt with a strong willed child like this? I've heard horror stories of parents who really came down hard on their kids and are still having constipation problems in Jr. High - I do not want to "scare" her into not pooping at all and go through the constipation thing - AGAIN (at least 4 times now). We do have a 6 month old but we've been dealing with this prior to me being pregnant. Any encouragement is greatly appreciated.