I also have an almost 3 year old daughter who has been "peeing on the potty" since April with maybe 3 accidents total... but she is scared of using the potty to poop.
She has not been a regular pooper since I stopped nursing her before her first birthday, but since the potty training it has gotten worse. She does the same thing with holding it in and we have done the suppository thing as well. Our doctor has told us to use Milk of Magnesia or the Miralax, but we had a hard time regulating the amounts without having her be too loose.
We are trying a more natural solution with having her eat yogurt daily(good bacteria cultures that help with digestion) these same bacteria cultures can be found in health food stores in a chewable form for toddlers (my daughter has 1 a day). I also mix ground flaxseed into applesauce or add it to muffins and pancakes. Lots of fresh and dried fruit also helps (my daughter loves fresh blueberries and melon and dried cherries). Having her adjusted by a chiropractor also helps. (My daughter has seen one since 6 weeks old because she was colicky.)
The mental part of the potty is still what gets my daughter, so we tell her that she can choose where to poop in the potty or a pull-up (she still wears them for nap and bedtime). 3/4 of the time it is still in a pull-up, but she is gradually "trying" on the potty. Encouraging the action and not the location has been a better solution for us right now. She will not be going to kindergarten and pooping in a pull-up, so eliminating some of the stress on her helps with the staying regular too.