M.P.
Sounds to that she is frightened about losing "part of herself" in the toilet. learning to use the potty chair or toilet involves emotions as well as physical readiness.
There have been many good suggestions to this sort of question asked by other mothers.
I sympathized with your dilemna. Potty training can be so difficult and society has put such a high premium on doing it the "correct" way. My advice is to just relax and go with the flow. (chuckle-literally) Tell her it's OK to poop in the potty chair or in her diaper. Take the pressure off of both of you. Don't ask her if she wants her diaper on or off. Just put it on and reassure it's alright to have it on. She may be trying to please you.
I would also add that 20 months is young to be fully potty trained. It's great she'll pee in the potty. Let her come around to pooping when she's ready.