In this work, we use hydrodynamical simulations to explore the effects of kinetic active galactic nuclei (AGN) jet feedback on the progression and outcome of the major merger of two isolated, gas-rich galaxies. We present simulations that use the moving-mesh code arepo to follow the progression of the merger through the first passage and up to the final coalescence, modelling the black holes at the centres of both of the merging galaxies using our prescription for black hole accretion via an α-disc and feedback in the form of a spin-driven jet. We find that the jets drive large-scale, multiphase outflows which launch large quantities of cold gas out to distances greater than 100 kpc and with velocities that reach . Gas in the outflows that decelerates, cools, and falls back on the galaxies can provide a rich source of fuel for the black hole, leading to intense episodes of jet activity in which the jet can become significantly misaligned. The presence of AGN jets affects the growth of the stellar component: star formation is moderately suppressed at all times during the merger and the peak of the star formation rate, attained during the final coalescence of the galaxies, is reduced by a factor of ∼2. Analysis of simulations such as these will play a central role in making precise predictions for multimessenger investigations of dual radio-AGN, which next-generation observational facilities such as LISA, Athena and SKA will make possible.