The home-use of a wearable artificial pancreas (AP) system requires an efficient and robust control algorithm. In this work, we propose a novel solution through an adaptive disturbance rejection approach. The controller features an observer that estimates the effect of improper clinical parameters and a feedback control law that builds on and compensates the estimated effect. Event-triggered data scheduling is designed for the state observer and the insulin-on-board estimate, to enable predictive control action for ascending and descending glucose traces. Besides, an event-triggered switching strategy is proposed to deliver insulin and glucagon separately. Glucose-and velocity-dependent parameter adaptation for the feedback control law are further introduced for each hormone infusion to address the asymmetric risks of hyperglycemia and hypoglycemia. The effectiveness and robustness of the controller are evaluated using the 10-adult cohort of the FDA-accepted UVA/Padova T1DM simulator. For scenarios with nominal basal rates and meal boluses, the proposed controller achieves satisfactory performance in terms of mean glucose and percent time in [70, 180] mg/dL without increasing the risk of hypoglycemia. The controller also behaves properly and safely with satisfactory performance for scenarios of moderate meal-bolus and basal rate mismatches. The results indicate the feasibility of achieving robust glucose regulation through an adaptive disturbance compensation approach for dual-hormonal AP systems.