Modifying the hexagonal lattices of graphene enables the repositioning and merging of the Dirac cones which proves to be a key element in the use of these materials for alternative electronic applications such as valleytronics. Here we study the nonequilibrium transport of carriers within a system containing two Dirac cones in both standard graphene and semi-Dirac graphene. In the latter, the lattice modifications cause the relativistic and parabolic dispersion bands to coexist, furnishing the Fermi surface with a rich pseudospin texture and a versatile Dirac cones separation. We construct a kinetic theory to investigate the carrier diffusion and uncover that the pseudospin index contributes to the particle current and, like the real spin, can induce a magnetoelectric effect, and argue that the pseudospin-charge coupling can be utilized to design a pseudospin filter. We explore the charge dynamics inside a quasi-one-dimensional conductor using the drift-diffusion model and detect the pseudospin accumulation at the sample boundaries. We find that, while, for graphene, the accumulation contributes to an extra voltage drop between the sample interfaces, the semi-Dirac system presents a similar accumulation that is strikingly equipped with valley polarization, signifying an essential tool for the control of valley manipulation and chirality transport using the pseudospin.