**Core Concept**
The question is testing the student's understanding of postpartum complications and their association with autoimmune disorders. The underlying concept involves the connection between pregnancy and the development of autoimmune diseases, particularly those involving coagulation and platelet disorders.

**Why the Correct Answer is Right**
The correct answer is Acquired Factor VIII inhibitors, also known as acquired hemophilia A. This condition is characterized by the development of antibodies against factor VIII, a crucial protein involved in blood clotting. Pregnancy is a known risk factor for the development of acquired hemophilia A, particularly in women with a history of autoimmune diseases. The presence of a skin rash and recurrent joint pains, combined with a family history of autoimmune disease, increases the likelihood of this diagnosis. The pathophysiology involves the formation of autoantibodies against factor VIII, leading to a deficiency in this protein and an increased risk of bleeding.

**Why Each Wrong Option is Incorrect**
**Option A:** Megakaryocytic thrombocytopenia refers to a condition characterized by a decrease in platelet count due to a problem with the megakaryocytes, the cells responsible for producing platelets. This condition is not directly related to pregnancy or autoimmune disease.

**Option B:** Amegakaryocytic thrombocytopenia is a rare congenital condition characterized by a severe decrease in platelet count due to a lack of megakaryocytes. This condition is not associated with pregnancy or autoimmune disease.

**Option C:** Functional platelet defect refers to a condition where platelets do not function properly, leading to an increased risk of bleeding. While this condition can be associated with various underlying causes, it is not directly related to the combination of pregnancy and autoimmune disease presented in the question.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that pregnancy can trigger the development of autoimmune disorders, including acquired hemophilia A. A high index of suspicion should be maintained in patients presenting with bleeding symptoms or a history of autoimmune disease, particularly in the postpartum period.

**Correct Answer Line**
✓ Correct Answer: D. Acquired Factor VIII inhibitors