We presented a theoretical study of the effects from two-side (2S) doing on low-temperature lateral transport in square quantum wells (QWs). Within a variational approach, we obtained analytic expressions for the carrier distribution, screening function, and autocorrelation functions for various scattering mechanisms. We found that the mobility of a 2S-doped square QW is larger than that of the one-side (1S) doped counter part for scattering from both interfaces or from the top interface. However, the former is smaller than the latter for scattering from the bottom (substrate-side) interface. The mobility of a 2S-doped square QW exhibits a well-width evolution slower than the power-of-six law characteristic of the undoped QW. The mobility may be enhanced by 2S doping. We examine the dependence of the enhancement factor on QW parameters for optimization of the structure. This factor may achieve an order of magnitude, which is much larger than that provided by earlier methods. Our theory is able to reproduce recent experimental data on transport in 2S-doped narrow square QWs, e.g., the mobility dependence on well width and the enhancement factor, which have not been explained so far.