Understanding the catalytic role of titanium-based additives on the reversible hydrogenation of complex metal hydrides is an essential step towards developing hydrogen storage materials for the transport sector. Improved bulk diffusion of hydrogen is one of the proposed catalytic effects, and here we study hydrogen dynamics in undoped and TiCl3-doped samples of NaAlH4 and Na3AlH6 using a combination of density functional theory calculations and quasielastic neutron scattering. Hydrogen dynamics is found to be limited and mediated by hydrogen vacancies in both alanate phases, requiring an activation in excess of 0.3 eV. Even at 390 K, less than 1% of the hydrogen in NaAlH4 performs long range diffusion, and only localized hydrogen dynamics is observed in Na3AlH6. The effect of the TiCl3 dopant on hydrogen bulk diffusion is found to be negligible.