Hospital readmissions within 30 days impose heavy clinical and financial burdens, linking unplanned returns to patient morbidity and cost inefficiency. Traditional models, logistic regression on aggregated features or RNNs over fixed windows, often lose temporal granularity, limiting their ability to capture nuanced patient trajectories. We propose DETER, a directed event-trajectory framework that models each ICU stay as a graph: nodes represent timestamped clinical events (vitals, labs, medications), and directed edges link successive events with learnable time-delta embeddings. A Temporal Graph Attention Network processes the full admission graph to produce dynamic patient embeddings. On MIMIC-III (14,532 admissions), DETER attains an AUC of 83.0% and an F1-score of 48.0 % for 30-day readmission prediction, outperforming BiLSTM baselines by +7.0% AUC and patient-similarity GCNs by +4.0% AUC. Ablation studies reveal that time-delta embeddings and sparse directed chains yield approximately 4% and 6% relative gains, respectively. Attention-weight visualizations highlight critical event transitions, such as creatinine rise to antibiotic dosing, that precede readmission. These results establish DETER as a novel and effective medium-term readmission model, demonstrating the value of event-chain graph representations in EHR analytics.