The evolution of an initially planar monolayer of charged microparticles in a complex plasma (plasma crystal) in horizontal (in the plane of the monolayer) and vertical parabolic confinements has been considered. The separation (buckling instability) of a Yukawa system into several layers at the weakening of the vertical confinement, as well as structural changes in such a plasma crystal, has been studied using the molecular dynamics method. In particular, it has been shown that the radial inhomogeneity of the plasma crystal qualitatively changes the character of the separation compared to homogeneous systems. Indeed, the separation begins in the center of the crystal, where the average distance between particles is minimal, and propagates in the form of a wave towards the periphery of the system at the weakening of the vertical confinement. This explains features of the behavior of plasma crystals in recent experiments with the complex plasma.