Poop potty training is just very scary to some children. Keep your dd in underwear, but let her ask for a diaper or pull-up to poop in. After several weeks of her asking for a diaper to poop in, select a day to begin poop potty training. On the appointed day, when she asks for a diaper, take her to the toilet instead. Since she'll have asked for a diaper, you'll know her urge to poop is strong, so take advantage of it. Of course you'll want to have some rewards on hand to minimize the trauma of achieving success!
If you think she'll withhold her poop when you poop potty train, you can give her a mild laxative daily while training to make it difficult to withhold.
FYI, there are two basic types of laxatives: stimulant and non-stimulant. Stimulant laxatives are often senna based (such as Senekot and ex-lax). They force bowel contractions to eliminate stool. The body can become dependent on stimulant laxatives, so they are for occasional use only. NON-stimulant laxatives hold water in the stool to prevent it getting dry/hard/difficult to pass. Non-stimulant laxative are not habit-forming (the body does not become dependent on them), so they are safe for long-term, daily use. Some good non-stimulant laxatives are Miralax, Benefiber, Milk of Magnesia and mineral oil. You can ask the pharmacist for guidance, if needed.
Robyn, Hi and welcome to the Toilet Teaching board.
The previous poster had a great idea. My suggestion would be to allow your DD to ask for a pull up when she needs to poop,but she must go into the bathroom, and be cleaned up as soon as she is done. Once she is comfortable a week, have her sit on the potty with her pull up on, and then get clean up as soon as she is done. After another week try cutting a hole towards the middle/back of the pull up, this way while on the potty most of the poop should fall into the potty. After a week, try without the pull up, if your DD seems like she still in uncomfortable, try putting a belt or something around her waist, as this is a comfort feeling for many children. It is a long drawn out process but with the small steps it is usually worth it in the end. I hope that helps. Please keep us updated on your DD progress.