The double-doped La2/3+4x/3Sr1/3-4x/3Mn1-xMgxO3 samples with fixed Mn^3+/Mn^4+ ratio equal to 2/1 are investigated by means of magnetism and transport measurements. Phase separation is observed at temperature higher than T^onset c for x = 0.10 and 0.15. For x = 0.10, rather strong phase separation induces drastic magnetic random potential and results in the localization of carriers. Thus, the varlable-range hopping process dominates. For other samples, there is no or only weak phase separation above T^onset c. Thus, thermal activation mechanism is responsible for the high temperature transport behaviour. For x = 0.20 and 0.25, unexpected AFM behaviour is observed at low temperature. All these results are well understood by considering the special role of the "double-doping".