Frequent and long-term exposure to hyperglycemia increases the risk of chronic complications, including neuropathy, nephropathy, and cardiovascular disease. Existing continuous subcutaneous insulin infusion (CSII) and continuous glucose monitoring (CGM) technologies model only specific aspects of glycemic regulation, such as predicting hypoglycemia and administering small insulin boluses. Similarly, current digital twin approaches in diabetes management primarily focus on predicting glucose responses to human behavior and insulin therapy. As a result, these technologies lack the ability to provide alternative treatment scenarios that could guide proactive behavioral interventions for optimal diabetes management. To address this gap, we propose GlyTwin, a novel computational framework that enhances digital twin technologies by integrating counterfactual explanations to simulate optimal behavioral treatments for glucose control. GlyTwin generates counterfactual treatments by recommending adjustments to behavioral choices, such as carbohydrate intake and insulin dosing, to significantly reduce the occurrence and duration of hyperglycemic events. In addition, GlyTwin incorporates stakeholder preferences into its intervention-generation process, ensuring that the tool is personalized and user-centric. We evaluate GlyTwin on AZT1D, a new dataset constructed by collecting longitudinal data from 50 individuals living with type 1 diabetes (T1D) on automated insulin delivery (AID) systems, each monitored for 26 days. Results show that GlyTwin outperforms state-of-the-art methods for generating counterfactual explanations, with 85.8\% valid explanations and 87.3\% effectiveness in preventing hyperglycemia compared with historical data.