We apply high resolution inelastic neutron scattering techniques, at cryogenic temperatures and up to near ambient temperatures, to study the microscopic dynamics of dihydrogen molecules, chemically bound in a RuH₂(H₂)₂[P(C₅H₉)₃)]₂ high-hydrogen content complex. At the lowest temperatures we first observe the quantum tunneling spectrum of the ground ortho-para hydrogen states. At slightly elevated and near ambient temperatures we observe the corresponding quasi-elastic scattering due to rapid proton exchange between the dihydrogen ligands and the hydrides. The overall energetics of the hydrides and the possible reaction paths for proton exchange are modelled with the use of hybrid density functional theory calculations.