Magnetization M and magnetoresistance Δρρ(H,T) (MR) were studied and MR analyzed quantitatively in the complicated low temperature Néel phase of RB12 (R - Ho, Er and Tm) antiferromagnets with structural (originating from cooperative Jahn-Teller effect) and electronic (coming from dynamic charge stripes) instabilities. It is shown, that well below the Néel field (HN) the magnetoresistance is determined by the concurrence of carriers' scattering by spin-density waves (leading to a linear positive contribution Δρρ(H) ∼ H) from one side, and by ferromagnetic nanoscale clusters (leading to a linear negative MR) from the other. The development of different kind instabilities in the critical region just below HN results into the emergence of an additional negative quadratic MR term, attributed to the carriers’ scattering on 4f-5d local electron density fluctuations. The anisotropy of both two linear and one quadratic MR components is analyzed in detail and compared for RB12 compounds with different magnetic structure.