We analyzed the confined donor states in elongated laterally coupled double Ga(Al)As craterlike shaped asymmetric quantum rings in the presence of electric and magnetic fields. We described a realistic non-uniform geometry of the structure and the distribution of the Al concentration along the vertical cross-section by special parameterized functions. Our calculations show that the in-plane electric field induces a strong mixing of confined donor states, resulting in a drastic alteration of the dipole moment and the polarizability of the structure induced by a displacement of the electron location toward the neighboring ring. In addition, we found that this effect can be controlled by applying a magnetic field along the growth crystal direction, providing a spike-like dependence of the electric polarizability of the structure.