We present the results of high-pressure transport measurements on the anion-mixed molecular conductors (DIETSe)2MBr2Cl2 [DIETSe = diiodo(ethylenedithio)tetraselenafulvalene; M = Fe, Ga]. They undergo a metal-insulator (M-I) transition below 9 K at ambient pressure, which is suppressed by applying pressure, indicating a spin-density-wave (SDW) transition caused by a nesting instability of the quasi-one-dimensional (Q1D) Fermi surface, as observed in the parent compounds (DIETSe)2MCl4 [M = Fe, Ga]. In the metallic state, the existence of the Q1D Fermi surface is confirmed by observing the Lebed resonance. The critical pressures of the SDW, Pc, of the MBr2Cl2 [M = Fe, Ga] salts are significantly lower than those of the the MCl4 [M = Fe, Ga] salts, suggesting chemical pressure effects. Above Pc, field-induced SDW transitions appear, as evidenced by kink structures in the magnetoresistance (MR) in both salts. The FeBr2Cl2 salt also shows antiferromagnetic (AF) ordering of d-spins at 4 K, below which significant spin-charge coupling is observed. A large positive MR change up to 150% appears above the spin-flop field at high pressure. At low pressure, in particular below Pc, a dip or kink structure appears in MR at the spin-flop field, which shows unconventionally large hysteresis at low temperature (T < 1 K). The hysteresis region clearly decreases with increasing pressure towards Pc, strongly indicating that the coexisting SDW plays an important role in the enhancement of magnetic hysteresis besides the random exchange interaction.