Your daughter sounds just like ours! LOL. She was dry through the night and peeing on the toilet at 18 months, very few accidents. But the idea of making a poop on the toilet frightened her, even at almost 3 1/2 years of age. One long-ago constipated attempt resulted in an association with, and fear of, pain. She is strong minded, and cannot be bribed. Even the temptation of something she wants very much would be shrugged off - we hope that means she'll have her own mind when she's a teen. But now, it makes it tricky for mom and dad to motivate her.
Ultimate success came in just 36 hours, unbelievable. First step: some days of sneaking Miralax into a drink once a day (2 tsp), per dr's orders. This softened her stool, and primed the pump, so to speak.
Her preschool teacher provided the magic key when she suggested creating a reward sticker chart. We shopped for an assortment of fancy stickers which she was allowed to choose, and decorated a chart with her own sparkly marker designs, wrote her name on top.
In order to remove the "poop only" association, our chart allowed her to place stickers for the following categories: I tried to go / No drips (in underpants) / I made a pee on the toilet / I made a poo on the toilet / Flushed toilet and washed hands.
We also wrote a list of rewards that she could achieve after a certain number of successful poops: for 5 poops, a small toy she had been wanting; same for 10; 15 a visit to the moon bounce; 20 going ice skating, etc. She chose the rewards herself, and thus had some control over the whole process.
36 hours in: her first poop. Not one subsequent poop ever went anywhere except the toilet again! We couldn't believe how easy it was, after many months of trying, frustration, poops in underwear, etc.
Once she had been successfully pooping on the toilet for some time, we shopped for pretty new underpants as a final reward. She's very proud of herself, and so are we.
Good luck!