In this work, chaotic vibrations of shallow sector-type spherical shells are studied. A sector-type shallow shell is understood as a shell defined by a sector with associated boundary conditions and obtained by cutting a spherical shell for a given angle , or it is a sector of a shallow spherical cap associated with the mentioned angle. Both static stability and complex nonlinear dynamics of the mentioned mechanical objects subjected to transversal uniformly distributed sign-changeable load are analyzed, and the so-called vibration charts and scales regarding the chosen control parameters are reported. In particular, scenarios of transition from regular to chaotic dynamics of the mentioned shells are investigated. A novel method to control chaotic dynamics of the studied flexible spherical shells driven by transversal sign-changeable load via synchronized action of the sign-changeable antitorque is proposed and applied. All investigations are carried out within the fields of qualitative theory of differential equations and nonlinear dynamics.