Hard round balls always indicate constipation. And yes, it's not uncommon for children to pass soft stool around hard stool that isn't passing. It's also very common for hard stools to have some blood on them. If the stool checks out okay, your pediatrician will probably recommend increasing fiber and fluids, giving a glycerine suppository or a small enema to get her cleaned out.
I was a pediatric nurse for more than 30 years, and this really sounds like some constipation to me. Your daughter is what, two or three? Around this time their appetite tends to decrease and sometimes they get busy playing and don't drink enough fluids.
Try to rest easy tonight, Mom.
Moderate to severe left-sided UC diagnosed 2001.
Flared for 5 years, finally in remission with Remicade since March 2006.
Avascular necrosis in both shoulders is my "forever" gift from steroids.
Colazal, Remicade, Nature's Way Primadophilus Reuteri.
"My life is an ongoing medical adventure"