Diabetes mellitus is a chronic metabolic disorder that has emerged as one of the major health problems worldwide due to its high prevalence and serious complications, which are pricey to manage. Effective management requires good glycemic control and regular follow-up in the clinic; however, non-adherence to scheduled follow-ups is very common. This study uses the Diabetes 130-US Hospitals dataset for analysis and prediction of readmission patients by various traditional machine learning models, such as XGBoost, LightGBM, CatBoost, Decision Tree, and Random Forest, and also uses an in-house LSTM neural network for comparison. The quality of the data was assured by preprocessing it, and the performance evaluation for all these models was based on accuracy, precision, recall, and F1-score. LightGBM turned out to be the best traditional model, while XGBoost was the runner-up. The LSTM model suffered from overfitting despite high training accuracy. A major strength of LSTM is capturing temporal dependencies among the patient data. Further, SHAP values were used, which improved model interpretability, whereby key factors among them number of lab procedures and discharge disposition were identified as critical in the prediction of readmissions. This study demonstrates that model selection, validation, and interpretability are key steps in predictive healthcare modeling. This will help health providers design interventions for improved follow-up adherence and better management of diabetes.