Advanced management algorithms are required in modern power systems to sustain energy supply with the highest availability and lowest cost. These algorithms need to be capable of not only maintaining scalability, tractability, and privacy, but also enabling the utilization of grid-edge aggregated flexibilities in transmission systems. This paper proposes a distributed hierarchical transactive energy management (TEM) scheme to manage peak load and line congestion problems using connected and aggregated flexibilities. In the scheme, resource owners can privately solve their respective preference problems and send their scheduled power to the corresponding node operator (NO). Afterward, NOs solve a coordination problem to harmonize the actions of resource owners at the same node. Meanwhile, the independent system operator (ISO) updates control signals to steer the scheduled power to a feasible and optimal point. To accomplish all these, a hybrid decomposition approach is further proposed based on consensus+exchange alternating direction method of multipliers (CE-ADMM) and dual decomposition (DD) (CE-ADMM+DD). Besides, a dynamically constrained cutting plane (DC-CP) update algorithm is evolved to control the feasibility condition and minimize sensitivity to initialization. The proposed hybrid decomposition approach is verified and its performance is compared with other reported approaches. Application to various networks verifies its scalability, enhanced accuracy, and convergence speed.