I went through this same issue with my youngest child. It was very frustrating for me. She was and is a very strong-willed and demanding person. I even did all the same things you have done, including having my doctor perscribe a laxative supplement, which I didn't really think was such a hot idea, given a healthy diet should be enough.
Unfortunately it is a vicious cycle. The more attention you give to the problem, the more your child uses this new found power for their purposes.
I'm going to suggest a radical idea. But first I need to warn you... a strong-willed child is tricky! 2nd, after having and raising 3 kids, my last child did not begin to have her bm's in a potty until she was almost 5! Talk about strong-willed!
Here's what finally worked for us, regarding the bm's. I made sure we had a quiet, non-threatening time at least once to twice a day for her to sit on the potty and I stopped bugging her about it. When she complained that she was in pain, I simply told her that she would not be in pain, if she would just go potty and let the poop come out when her body told her it needed to come out.
This didn't happen over night. She's almost 8 now. She still goes through bouts where she avoids eliminating. Not due to pain, just failure to make the time to sit, because she has attention challenges. When this happens, she still has minor accidents. I don't make a big deal of it. I sympathize with her and showed her how to clean up herself and just make sure she does a good job. Once she discovered I wouldn't clean her up after too many accidents... she decided the work was not worth the mess and we nipped the problem in the bud.
But I must warn you... in dealing with a 2-3yo, you don't have the same ability to reason as with a 5 yo. You may need to forgo the potty training issue until you get her confident to just have a bm and then begin again.
I was frustrated at how long it took me to potty train my last child. I think it would have taken less time, if I had been able to hide my frustration from her. It really was 80% power & 20% fear; 100% her choice.
Hope that helps you.
P.S. I've never met a 3rd grader that still wore diapers.. In fact, I've never met a 1st grader that was still in diapers.... so maybe just relax and let her think it's not a big issue to you anymore... just don't reward her with more of your attention by witholding a bm.