Our youngest and our only daughter both have this problem - constipation is a vicious vicious cycle... the first time is simply, for whatever reason, it hurts to poop - then they start holding it, which makes it hurt more. That can lead to an impacted colon, which ultimately takes away any "urge" to go.
The fact that she doesn't want to go sitting on the potty (I'm guessing she's standing when she goes in her diaper) implies that she might have the beginnings of hemmohroids (spelling?). You might want to talk to her pediatrician about checking, and using PrepH if that is the case.
We've found that between a half a cup and a full cup of ginger ale every day has enough sugar in it to pull water into the intestines (just like mom, but not as diarrhea inducing). Making sure they drink enough fluids is essential, too, because dehydration directly causes constipation.
With the baby we've also found that a chiropractor helps. Call them quacks if you wish, but until very recently the only time he defecated was after a visit to the chiropractor - he would go normally for 2 or 3 days, and then stop until he went again. For a while we were going twice a week, then as the intervals of 'normal poop' got longer we started going once a week, then every two weeks - now we go once every 3 - 4 weeks. Between that and the ginger ale we really haven't had any problems with hard stool or constipation.
Good luck with your angel.