The effect of higher-order corrections to the Born approximation is studied for the previously obtained giant conductance enhancement in tunnel-coupled double quantum wires in a magnetic field by including both impurity and interface-roughness scattering. The enhancement is caused by an abrupt suppression of back-scattering of electrons which occurs when the chemical potential is in the anticrossing gap of the ground tunnel-split doublet. The calculated conductance enhancement is large, and the relative higher-order correction to the enhancement is found to be significant for long-range scattering potentials. However, this relative higher-order correction will be reduced as the range of scattering potentials becomes small. The correction depends on various effects, such as the magnetic field, electron and impurity densities, impurity positions, symmetric and asymmetric doping profiles, centre barrier thickness, and degree of interface roughness.