My daughter is almost 3 1/2 and she is the same way despite having been potty trained for around a year now. Pooing is an ordeal in our house, and like your daughter she is on Myralax because she will hold it for so long. The doctor classified her as anal retentive, and this tends to be a comment trait among females on my mothers side of the family. I think part of it is that she was exclusively breastfed for a long time, and as a baby she could go two weeks without pooing, which is normal for a breastfed baby. By the time she was potty trained she was still only going once every three days.
We had her on 17mg-which is a full dose-for awhile and she actually got in the habit of pooing every day, and it was becoming less of an issue. She had CA-MRSA last recently, and I stopped giving her the Myralax because of the antibiotics and their side effects so pooping has once again become an issue.
So what we're doing is the 17mg, fiber cereal, no constipating foods like bananas and lots and lots of patience and time and books as I take her in there when I notice the signals she has to go and we sit and she pouts about it, but I am calm and just tell her she has to go. If she does go, we make a huge ordeal out of it, call Daddy so she can tell him, she might get a treat like a fruit popsicle, or we'll read an extra book at break or bed time-things like that. It took around a month last time for this to set in, and once it did she was going about three times a day, regularly without tears. And books-there are some great books out there on going potty, but one of my daughters favorites is Everybody Poops. It puts the issue on a level that makes it fun for kids.
I can also tell you this, I dont have to worry about poo incidents while we're away from home. She will only poo at home, and I can name several women in my family who are the same way. So you might find that even if you do get this straightened out by the time she hits preschool she might not poo while she is there anyways. So you might want to start a routine where she goes first thing in the morning and in the evenings.
Good luck, I really understand how frustrating this can be and I hope our situation has helped you some.