We investigate a spinful double quantum dot coupled to leads in a pseudospin valve configuration. The interplay of interaction and interference produces, in the stability diagram, a rich variety of current resonances modulated by the system parameters. In the presence of ferromagnetic leads and pseudospin anisotropy, those resonances split, turn into dips, and acquire a Fano shape, thus revealing a synthetic spin-orbit interaction induced on the double quantum dot. A set of rate equations derived for a minimal model captures those features. The model accurately matches the numerical results obtained for the full system in the framework of a generalized master equation and calculated within the next to leading order approximation.