I guess my first question would be to say...why are you letting where your daughter poops have such control over your emotions? Does it really make a difference over the long haul if it takes them 2 years or 4 years to learn to poop on the pot? I've never heard of a child who didn't have a physical reason for using diapers going to kindergarten in diapers, or even getting close to that age without using the toilet.
I never did the whole potty training thing. I have 5 kids and the first 3 decided to start using the potty when they turned 3 (all boys) and rarely had accidents. Now I have a 3 year old girl and she absolutely refuses to go on the potty at all. I really don't want to force it, although I would love to go back to buying diapers for only one child. I'm planning on sending her to preschool a few days a week next fall, and if she is not potty trained by then she will not be able to go to school. We have started talking with her about it now. She is very familiar with the concept of school, so I have been telling her that when she is big enough to go on the potty, she is big enough to get to go to school. Hopefully she will make that step as we get closer to fall.
Although she is my 4th child, this is the first time that I have had one not want to use the potty at all. If your daughter tolerates wearing underwear (mine just sits in place and screams if I put underwear on her), then I would suggest having her wear underwear while home, diapers or pull ups when leaving the house. That way you are not cleaning up a mess when you are out. That's just me. I'd rather change a diaper than clean up after a major accident.
I'm sure as a single mom you are getting lots of unsolicited advice about this topic, and that may be putting pressure on you or make you feel like you are doing something wrong, but it sounds to me like you are a great mom who has tried many things and maybe you are overinvested emotionally in the whole potty training thing. I try to think about it like this...I don't want my husband telling me when and where I should relieve myself, so why would I force my child? This is intensely personal for the child. When she is ready, she will do it. If she sees it upsetting you suddenly it does become a control issue, and one that she wants to win. Kids love to find something that makes you crazy and then use it whenevery convenient for them. I would say, don't give her that much power over you. Don't make a big deal about it, actually make it a non issue, and I believe she will get bored of it and just do it. She obviously knows what to do and even how to do it. Hope some of what I said (or even all of it!) will be of some help to you. Good luck with that.