A novel concept to facilitate the ignition of low-volatility gelled hypergolic propellants (GHPs) is to inject the fuel and oxidizer as two unequal-size jets such that the resulting impingement would involve the insertion of one liquid element into another. This should lead to rapid internal mixing and consequently liquid-phase reaction. In this study we have computationally simulated the headon collision and coalescence between two droplets of unequal sizes, using the front-tracking technique. The mixing process after coalescence is also simulated by tracing colored particles embedded in the droplets. Moreover, we have developed a novel method to transfer the surface energy of the merged interface to the kinetic energy of the neighboring liquid, in order to keep the total energy conserved. This method has been verified to successfully characterize the coalescence process of two equal-size droplets, in which the previously neglected merged interface energy has been shown to quickly dissipate. For the unequal-size case, the merged interface energy is crucial to the mixing of the droplets. Our method enables us to capture the salient feature of mixing, i.e., the occurrence of mushroom-like jet structure, which has previously been observed in experiments. Such structure will not emerge if the merged interface energy is neglected.