Difficulty-controllable question generation for reading comprehension has gained significant attention in the field of education as a fundamental tool for adaptive learning support. Although several neural question generation methods have recently succeeded in controlling difficulty, conventional approaches still face two major limitations. First, they cannot directly generate multiple-choice questions, which are the most widely used question type in educational contexts. Second, they are not explicitly trained to optimize the accuracy of difficulty control, leaving room for further improvement in difficulty controllability. To address these limitations, this study proposes a novel difficulty-controllable multiple-choice question generation method for reading comprehension which leverages a large language model trained using a direct preference optimization technique to improve the accuracy of difficulty control.