**Core Concept**
The patient's presentation suggests a severe obstetric complication, likely involving uterine damage or placental abruption leading to hemorrhage. The history of difficulty in placental removal and 'uterine handling' during delivery hints at a possible uterine injury.

**Why the Correct Answer is Right**
The most probable diagnosis is uterine inversion, a condition where the uterus turns inside out, often as a result of excessive traction on the umbilical cord or placenta during delivery. This can lead to severe hemorrhage, shock, and potentially life-threatening complications. The history of difficulty in placental removal and 'uterine handling' during delivery increases the likelihood of uterine inversion.

**Why Each Wrong Option is Incorrect**
* **Option A:** Placental abruption, while a possible cause of heavy bleeding, typically presents with pain and possibly fetal distress, but the history of uterine handling during delivery makes it less likely.
* **Option B:** Postpartum hemorrhage (PPH) is a possibility, but the specific history of difficulty in placental removal and 'uterine handling' during delivery suggests a more specific and severe complication like uterine inversion.
* **Option C:** Uterine atony is a common cause of PPH, but it would not typically present with a visible fleshy mass protruding from the vagina.

**Clinical Pearl / High-Yield Fact**
Uterine inversion is a medical emergency requiring immediate recognition and treatment, often involving manual replacement of the uterus or surgical intervention to prevent further complications and hemorrhage.

**Correct Answer:** C. Uterine inversion.