We present optical and near-infrared integral field spectroscopy of the SCUBA galaxy SMMJ163650.43+ 405734.5 (ELAIS N2 850.4) at z = 2.385. We combine Ly alpha and H alpha emission line maps and velocity structure with high-resolution HST ACS and NICMOS imaging to probe the complex dynamics of this vigorous starburst galaxy. The imaging data show a complex morphology, consisting of at least three components separated by similar to 1 arcsec (8 kpc) in projection. When combined with the Ha velocity field from UKIRT UIST IFU observations we identify two components whose redshifts are coincident with the systemic redshift, measured from previous CO observations, one of which shows signs of AGN activity. A third component is offset by 220 +/- 50 km s(-1) from the systemic velocity. The total star-formation rate of the whole system ( estimated from the narrow-line H alpha and uncorrected for reddening) is 340 +/- 50 M-. yr(-1). The Ly alpha emission mapped by the GMOS IFU covers the complete galaxy and is offset by + 270 +/- 40 km s(-1) from the systemic velocity. This velocity offset is comparable to that seen in rest-frame UV-selected galaxies at similar redshifts and usually interpreted as a starburst-driven wind. The extended structure of the Ly alpha emission suggests that this wind is not a nuclear phenomenon, but is instead a galactic-scale outflow. Our observations suggest that the vigorous activity in N2 850.4 is arising as a result of an interaction between at least two dynamically-distinct components, resulting in a strong starburst, a starburst-driven wind and actively-fuelled AGN activity. Whilst these observations are based on a single object, our results clearly show the power of combining optical and near-infrared integral field spectroscopy to probe the power sources, masses and metallicities of far-infrared luminous galaxies, as well as understanding the role of AGN- and starburst-driven feedback processes in these high-redshift systems.