K.,
As others here have stated and as people have previously told me, pooping seems to be more difficult for kids. I have a daughter who is almost 4 and was completely potty trained before she was 2, no issues at all and she did it herself (no pushing from me). I have a son who will be 2 in a couple of days and sometimes he'll really interested in using the toilet (like in the middle of the night when he wakes up crying because he needs to go), but other times he's not (like first thing in the morning when his diaper is actually dry).
The one thing I used for both of them is books, especially for BMs. You mentioned your daughter will say she needs to go, but then want off the toilet before the deed is done, only to go in her panties. I think that has to do with the short attention span (my son does the same thing) and if you can get her to sit on the toilet longer she may have better success. It will also distract her mind from pooping and any negativity she has associated with it.
Good luck and although it is frustrating for you, I encourage you not to use pull-ups or diapers, that may be more frustrating for your daughter. Just as you don't want to start power struggles over food, you don't want to start them over toileting issues.
D.