We have extended the applicability of the two-step approach to higher-dimensional problem, and have further developed it to evaluate the quantum dynamics and stationary states of a general class of coupled anharmonic oscillator system. This new approach has enabled us to investigate the topic of continuous variable entanglement within these coupled oscillator systems with good numerical efficiency. In particular, we have applied it to study the relation between entanglement, squeezing, and quantum uncertainties, of the systems’ ground states. Interestingly, while the relation between quadrature squeezing and entanglement depends sensitively on the nonlinear potential, the influence of nonlinear perturbation on the entropy-uncertainty relation is minimal, especially when the entanglement between the two oscillators is large. We have also explored into the dynamics of entanglement where we have found that entanglement dynamics can depend completely on the global classical dynamical regime, without being influenced by the local classical behavior.