We have performed two-dimensional two-fluid simulations including finite electron inertial effects to investigate the cross-scale coupling in the evolution of MHD-scale Kelvin-Helmholtz (KH) mode. We focus on the model in which density is uniform and only the in-plane magnetic field component is present. The effects of the velocity jump across the shear layer and those of the variation of the magnetic field intensity across the shear layer are considered. When the shear is strong enough to make a KH vortex highly rolled-up, within-the-vortex reconnection is seen to play crucial roles in determining the structure of the large-scale vortex itself. Especially when the magnetic field intensity is significantly unbalanced across the shear layer, injection of a magnetic bubble is seen to result from the reconnection process.