We present new, high-angular resolution interferometric observations with the Karl G. Jansky Very Large Array of 12CO J = 1−0 line emission and 4–8 GHz continuum emission in the strongly lensed, z = 2.3 submillimetre galaxy, SMM J21352-0102. Using these data, we identify and probe the conditions in ∼100 pc clumps within this galaxy, which we consider to be potential giant molecular cloud complexes, containing up to half of the total molecular gas in this system. In combination with far-infrared and submillimetre data, we investigate the far-infrared/radio correlation, measuring qIR = 2.39 ± 0.17 across SMM J21352. We search for variations in the properties of the interstellar medium (ISM) throughout the galaxy by measuring the spatially resolved qIR and radio spectral index, αradio, finding ranges qIR =[2.1, 2.6] and αradio = [−1.5, −0.7]. We argue that these ranges in αradio and qIR may reflect variations in the age of the ISM material. Using multi-J 12CO data, we quantitatively test a recent theoretical model relating the star formation rate surface density to the excitation of 12CO, finding good agreement between the model and the data. Lastly, we study the Schmidt–Kennicutt relation, both integrated across the system and within the individual clumps. We find small offsets between SMM J21352 and its clumps relative to other star-forming galaxy populations on the Schmidt–Kennicutt plot – such offsets have previously been interpreted as evidence for a bi-modal star formation law, but we argue that they can be equally well explained as arising due to a combination of observational uncertainties and systematic biases in the choice of model used to interpret the data.