**Core Concept**
The patient's symptoms suggest a disorder affecting the **extraocular muscles** or their **innervation**, specifically involving the **medial longitudinal fasciculus (MLF)**. This structure is crucial for **conjugate eye movements**, including adduction.

**Why the Correct Answer is Right**
Given the patient's presentation with **diplopia**, **limitation of adduction** in one eye, and an **abducting saccade** in the other, along with **preserved convergence**, the most likely diagnosis is **internuclear ophthalmoplegia (INO)**. INO is characterized by a lesion in the **MLF**, which disrupts coordination between the **oculomotor nucleus** (responsible for adduction) and the **abducens nucleus** (responsible for abduction), leading to the observed symptoms.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because it doesn't specifically relate to the symptoms described.
**Option B:** Incorrect as it doesn't typically present with preserved convergence.
**Option C:** Incorrect because it usually involves other cranial nerves and doesn't specifically cause the adduction limitation with abducting saccade.
**Option D:** Incorrect as the description doesn't match the classic presentation of a third nerve palsy.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that **convergence** is often **preserved** in INO because it involves a different pathway than the MLF, allowing for near vision to remain intact despite the disorder affecting conjugate eye movements.

**Correct Answer:** D. Internuclear ophthalmoplegia.