M.R.
It sounds like you're setting yourself up for a huge power struggle that, no matter what you do, you will never be able to win.
Why? Your daughter has control over her bowels, not you. She gets to decide if and when she uses the potty and it is likely that she knows it is frustrating for you. She throws the poop? Calmly clean it up and don't make a big deal. It sounds like everything she is doing gets a big ole rise out of you - sounds like a fun game for a 3 year old, doesn't it? She really does have control over the situation; the situation being "let's see how much attention, negative or positive, I can get from mommy!"
Back off and let her take the lead. She'll go when she is ready. Pushing her and forcing her to do what YOU want her to do instead of what SHE is ready to do will only backfire. You could even put away the potty movies, the potty books, the potty chairs, the new big girl underwear. When she's ready, ask her if she's ready to be a big girl and try again. If not, then wait.
Edited to add - you guys are so sweet!