Using the effective mass and parabolic band approximations, the binding energy of a shallow donor impurity is calculated in a GaAs-(Ga,Al)As quantum well wire of rectangular transversal section, under the combined effects of two independent axially-applied intense laser radiation fields and a static electric field oriented in the cross-section plane. The lateral size of the rectangular cross-section is assumed to be larger than 10 nm, in such a way that the uncorrelated electron motion along the x and y directions can be considered uncoupled. The impurity-related states are calculated by means of a variational procedure using a three-dimensional hydrogen-like trial wave function. The intense laser field effects are introduced via the combination of the Floquet method for the laser-modified confinement potential shape and the inclusion of a two-interaction centers model for the Coulombic coupling. It is shown that, according to the polarization of the incident radiation, the quantum well wire can evolve from a single 1D-heterostructure towards a configuration of two-well defined or four-well defined laser-induced parallel coupled quantum well wires. The obtained results also show that the binding energy is strongly dependent on the impurity position and on the strength of the intense laser field parameter.