Why wont my 4 year old poop in the toilet?!

Ok, so I'm at my wits ends here. My daughter is 4 and a half years old and has NO interest in learning how to only poop on the toilet. I feel like I've tried everything! We've tried giving her a treat when she's successful, setting a timer to make her go, sing a special potty song, give her toys to play with while she sits, completely cold turkeyed pull ups, set up a sticker chart with a big prize at the end, and even letting her sit with it on her butt (at a MAX of 5 minutes). She has always showed interest at first before not caring anymore and she doesn't care how it feels on her butt. We also know that she knows when she needs to go because she will always find a corner or a spot to stand still in while she does and everytime we notice it, we have rushed her to the bathroom. I've even done timeout and taken away privileges on a smaller scale. Any suggestions for a overwhelmed mom with an extremely stubborn kid?