We report on coherent enhancement of two-photon emission from the excited vibrational state of molecular hydrogen triggered by irradiating mid-infrared pulses externally. We previously observed the two-photon emission triggered by the internally generated fourth Stokes photons. By injecting independent mid-infrared pulses externally, it is possible to control the experimental parameters and investigate the mechanism in more detail. In this article, we describe the two-photon emission using the external trigger pulses. Its spectrum and dependence on the energy and timing of the trigger pulse are presented along with numerical simulations based on the Maxwell-Bloch equations. The measured number of emitted photons is 6 x 10(11) photons/pulse and the resulting enhancement factor from the spontaneous emission is more than 10(18). This value is three orders of magnitude higher than that of the previous experiment. External control of the emission process is expected to be essential for observation of the weaker process of radiative emission of a neutrino pair.