The plasma dynamics resulting from the simultaneous impact, of two equal, ultra-intense laser pulses, in two spatially separated spots, onto a dense target is studied via particle-in-cell simulations. The simulations show that electrons accelerated to relativistic speeds cross the target and exit at its rear surface. Most energetic electrons are bound to the rear surface by the ambipolar electric field and expand along it. Their current is closed by a return current in the target, and this current configuration generates strong surface magnetic fields. The two electron sheaths collide at the midplane between the laser impact points. The magnetic repulsion between the counter-streaming electron beams separates them along the surface normal direction, before they can thermalize through other beam instabilities. This magnetic repulsion is also the driving mechanism for the beam-Weibel (filamentation) instability, which is thought to be responsible for magnetic field growth close to the internal shocks of gamma-ray burst jets. The relative strength of this repulsion compared to the competing electrostatic interactions, which is evidenced by the simulations, suggests that the filamentation instability can be examined in an experimental setting.