Its normal I guess, but still to be on safe side, I would recommend you take/show your daughter to the HV/ Doctor. One of my twins had a milky white discharge from her vagina two days after birth. I panicked and took her to the doctor, who said not to worry. Only if there is a foul smell coming from the discharge; then there may be an infection. As you said, its all due to hormones. Bleeding after birth or few days after is okay. What I want to know is: If it is just a few drops or heavy bleeding. If its the former,then its perfectly normal.
Dont worry. It will stop eventually. While cleaning her vagina, just spread the labia a bit and gently clean the creases with luke warm water and no need to dig deeper as it may hurt the baby.