The energy spectrum of two electrons spatially separated in two vertically coupled quantum rings under hydrostatic pressure and magnetic field is calculated. In order to study the two-electron properties, the adiabatic approximation is used by considering quantum rings with square cross-sections. The changes of the energy level-ordering and the crossover among the curves as a function of radii and ring-ring separation as well as the hydrostatic pressure and magnetic field are discussed. The effects related to the geometry of the rings as well as the external fields on the crystal Wigner formation are analyzed. Additionally, it is checked that the present results are in good agreement with those previously obtained for the limit cases corresponding to zero ring-ring separation and rings of equal center line radius.