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In this paper, an event-triggered time-varying formation tracking control for a class of second-order nonlinear multi-agent systems (MAS) operating within a constrained region is investigated. To mitigate the negative effects of external unknown disturbance, a novel disturbance observer with performance guarantees is proposed, enabling precise disturbance estimation. Using the artificial potential field (APF) method, a repulsive potential function is introduced to prevent inter-agent collisions as well as collisions with environmental obstacles. To reduce continuous communication and frequent system updates, a sliding mode technique is incorporated into the formation tracking controller, utilizing an event-triggered mechanism. The controller is also applicable to the formation control of MAS in switching-constrained regions. The achievement of the specified time-varying geometric formation is rigorously demonstrated through the Lyapunov framework. Numerical simulations are presented to validate the effectiveness of the theoretical results.