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We introduce a Y-configuration model for a double quantum dot (QD) system, which is modeled for Kerr nonlinearity using the density matrix theory. Inhomogeneity in QDs is included in the calculations of the real part (Kerr) and the imaginary part (absorption) of the density matrix, which has not been covered before in Kerr calculations. Five configurations are studied: Y, ladder, Λ, staircase, and weak probe. Frequency detunings, controlling fields, and phases are used to study the structures. Our system shows high controllability as well as a giant Kerr dispersion, propagation without distortion, wide electromagnetic induced transparency, and switching between subluminal to superluminal propagation by tuning its fields.