I also used glycerine suppositories for my daughter when she was a baby under the advice of her pediatrician. Fortunately I only had to use them a few times. The white part you saw may have been the suppository itself coming back out as they begin to melt very quickly inside a warm little tushy and get very slippery. My pediatrician was wonderful and tended to take holistic approaches whenever possible. He didn't hesitate for a second to recommend the suppositories and I'm so glad I followed his advice. A constipated baby is a miserable baby and can lead to other complications.
I think suppositories are very helpful in that they aren't something that has to be ingested or digested...they work from the other end. Every baby is different and like I said, I only had to use them a few times, but if she is doing what her doctor has recommended, I think she's doing the right thing.