The dissociative ionization of N2O by near-single-cycle laser pulses is studied using phase-tagged ion-ion coincidence momentum imaging. Carrier-envelope phase (CEP) dependences are observed in the absolute ion yields and the emission direction of nearly all ionization and dissociation pathways of the triatomic molecule. We find that laser-field-driven electron recollision has a significant impact on the dissociative ionization dynamics and results in pronounced CEP modulations in the dication yields, which are observed in the product ion yields after dissociation. The results indicate that the directional emission of coincident N+ and NO+ ions in the denitrogenation of the dication can be explained by selective ionization of oriented molecules. The deoxygenation of the dication with the formation of coincident N-2(+) + O+ ions exhibits an additional shift in its CEP dependence, suggesting that this channel is further influenced by laser interaction with the dissociating dication. The experimental results demonstrate how few-femtosecond dynamics can drive and steer molecular reactions taking place on (much) longer time scales.