Recent climate changes, driven by greenhouse gas emissions, along with global regulations aimed at mitigating these effects, have intensified research on carbon-free fuels. Among these, hydrogen stands out as one of the most promising options. In this study, use is made of a recent 1D kernel expansion model developed by the authors, which is based on the conservation equations of mass, energy and deficient reactant. The theory of transient thermo-diffusion is also adopted to estimate the reactant and temperature gradients at the outer flame surface. The kernel expansion model accounts for the variability of thermodynamic properties both inside and outside the flame volume, including high-temperature ionization and dissociation effects. The kernel expansion model is used until the non-linear stretch effects are sufficiently relaxed. Subsequently, the propagation of the premixed flame is described by means of a two-zone combustion model. During both phases, the effects of hydrodynamic and thermo-diffusive instabilities are accounted for. The former are modeled considering the flame wrinkling produced by the density discontinuity across the flame, evolving towards a self-similar fractal-like behavior. The latter, induced by a less-than-unity Lewis number, are modeled introducing an equivalent flame consumption speed to quantify the increase in flame expansion velocity. The model is validated against experimental data from literature obtained for premixed hydrogen-air flames propagating in an optically accessible spherical bomb. The data used for model validation refer to quiescent conditions at multiple lean equivalence ratios (from 0.45 to 0.97). The capabilities of the present model are assessed with reference to the measured time histories of chamber pressure, flame radius and expansion speed. A good agreement is achieved across all the test cases considered, confirming the consistency of the integrated ignition-combustion model proposed in this work.