We present ~0.15'' spatial resolution imaging of SHiZELS-14, a massive (M*~10^11 M_sol), dusty, star-forming galaxy at z=2.24. Our rest-frame ~1kpc-scale, matched-resolution data comprise four different widely used tracers of star formation: the H-alpha emission line (from SINFONI/VLT), rest-frame UV continuum (from HST F606W imaging), the rest-frame far-infrared (from ALMA), and the radio continuum (from JVLA). Although originally identified by its modest H-alpha emission line flux, SHiZELS-14 appears to be a vigorously star-forming (SFR~1000 M_sol/yr) example of a submillimeter galaxy, probably undergoing a merger. SHiZELS-14 displays a compact, dusty central starburst, as well as extended emission in $\rm{H}\alpha$ and the rest-frame optical and FIR. The UV emission is spatially offset from the peak of the dust continuum emission, and appears to trace holes in the dust distribution. We find that the dust attenuation varies across the spatial extent of the galaxy, reaching a peak of at least A_H-alpha~5 in the most dusty regions, although the extinction in the central starburst is likely to be much higher. Global star-formation rates inferred using standard calibrations for the different tracers vary from ~10-1000 M_sol/yr, and are particularly discrepant in the galaxy's dusty centre. This galaxy highlights the biased view of the evolution of star-forming galaxies provided by shorter wavelength data.