The last thing you want is a huge power struggle over this. It's so hard as a parent to see your child regress when they were doing so great and not get completely frustrated. Try to take a step back & emotionally distance yourself from this phase (that's all it is!) so you don't get too upset up over it. Your daughter picks up on how you feel & knows she can get your goat- hence the Elmo comment.
Things to try:
Have her sit on the potty shortly after lunch (or breakfast or even dinner depending on her b.m. schedule) & either give her some books to look at or hang out with her & read to her (to encourage her to sit a little longer)- hopefully, you can encourage her to have a b.m. at that time (especially before afternoon nap- this is what I did with my 29 month old son & he now naps without a diaper- yay!).
Wake her up a little earlier in the morning & put her on the potty right away (to "catch" her before she poops/pees).
It sounds like she's pretty regular- maybe you just need to encourage her to sit on the potty longer & hang out a little to get her to poop. They get so busy playing & learning all day, sometimes they hold it in & don't really realize they have to poop until they get some down time in their crib for nap or quiet early morning time when their little bodies are waking up & thier minds aren't racing.
She could also just have had or is on the verge of having a huge cognitive growth spurt (or a physical one) which I find always throws my guys out of whack (sleeping, eating, moods, etc.) for a few weeks. Just when you're in a good groove... :)
It's all about control too- theirs, so maybe let her pick out the books you'll read while she sits on the potty, let her pick out her underpants when she gets dressed, etc. to keep a positive spin on her spending a little more (forced by Mama) time on the potty. You can bill it as some time for just the 2 of you sans baby (if that's possible), of course, you don't want that to backfire & she's on the potty 24/7 to have alone time with you! :)
Personally, I'd do away with rewards altogether. We never used them with either of my sons other than words of encouragement, applause & thumbs-up. The younger one p. trained much earlier (27 mos.) than the older one (who was 3+).
We also leave the crib rail down so that the younger one can climb out & get me or my husband if he needs to use the potty (during nap/night). He still wears a diaper at night, though wakes up dry most mornings. He does climb out in the morning & we take off his diaper so he can go potty 1st thing.
We keep a night light on in the bathroom for my older son who will wake-up & go if he needs to. Maybe you could also try waking her in the night (just before you go to bed) and have her use the potty to get her body used to the sensation & start to transition her to sleeping without a pull-up. My personal theory- no pull-up, no poop! At 3+ she's vain enough to want to keep her lovely p.j.'s/underpants clean. It took a really long time to night train (wetting only) my older son since he was such a hard sleeper. I'm hoping it'll be easier with #2 as he seems to have more control.
Good Luck- hope some of this helps. Don't worry, she won't be pooping in her pull-up forever- in a few months, you'll forget why this irked you so much!
S.