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The $\Lambda$CDM paradigm successfully explains the large-scale structure ofthe Universe, but is less well constrained on sub-galactic scales.Gravitational lens modelling has been used to measure the imprints of darksubstructures on lensed arcs, testing the small-scale predictions of$\Lambda$CDM. However, the methods required for these tests are subject todegeneracies among the lens mass model and the source light profile. We presenta case study of the unique compound gravitational lens SDSSJ0946+1006, whereina dark, massive substructure has been detected, whose reported highconcentration would be unlikely in a $\Lambda$CDM universe. For the first time,we model the first two background sources in both I- and U-band HST imaging, aswell as VLT-MUSE emission line data for the most distant source. We recover alensing perturber at a $5.9\sigma$ confidence level with mass$\log_{10}(M_\mathrm{sub}/M_{\odot})=9.2^{+0.4}_{-0.1}$ and concentration$\log_{10}c=2.4^{+0.5}_{-0.3}$. The concentration is more consistent with CDMsubhalos than previously reported, and the mass is compatible with that of adwarf satellite galaxy whose flux is undetectable in the data at the locationof the perturber. A wandering black hole with mass$\log_{10}(M_\mathrm{BH}/M_{\odot})=8.9^{+0.2}_{-0.1}$ is a viable alternativemodel. We systematically investigate alternative assumptions about thecomplexity of the mass distribution and source reconstruction; in all cases thesubhalo is detected at around the $\geq5\sigma$ level. However, the detectionsignificance can be altered substantially (up to $11.3\sigma$) by alternativechoices for the source regularisation scheme.

Gravitational imaging through a triple source plane lens: revisiting the $\Lambda$CDM-defying dark subhalo in SDSSJ0946+1006