Quadrotor unmanned aerial vehicles (UAVs) are widely utilized for various low-altitude tasks. However, precise attitude tracking performance is restricted by external interferences and internal model uncertainties, including unmodeled aerodynamic characteristics, parameter drifts, and time-varying environmental loads. To address the piecewise discontinuous lumped disturbances caused by low-altitude turbulence, this paper proposes improved schemes based on the mature dual-layer adaptive high-order sliding mode framework. A dual-layer nested adaptive strategy is constructed, where the first layer adjusts the amplitude of switching gain in control laws, and the second layer adaptively tunes time-varying parameters to limit the gain variation rate. This design eliminates the requirement for prior upper bound information of disturbances and their derivatives. Sufficient conditions for sliding mode existence under piecewise discontinuous lumped disturbances are derived in this work. The considered disturbances are piecewise discontinuous with uniformly bounded second derivatives in each interval, which better matches the real low-altitude gust flight scenarios of quadrotors. A unified composite Lyapunov function is constructed to simultaneously analyze the finite-time convergence of sliding variables, adaptive deviations, and disturbance observation errors, which simplifies the stability deduction process of the closed-loop system. Multiple segmented composite gust disturbances and parameter perturbation simulation cases are established. Combined with two-dimensional and three-dimensional phase trajectory visualization methods, multi-dimensional quantitative evaluation of the controller is realized. Based on homogeneity theory and Lyapunov analysis, the finite-time stability of the closed-loop system is proven, and MATLAB numerical simulations fully verify the comprehensive control performance of the proposed controller.