We model a core-shell quantum dot using a one dimensional system of two interacting electrons with a potential that can vary from one corresponding to a dot with comparable width of core and shell to one where the core well width becomes very small, but is always non-zero, while the shell becomes wide. We calculate the entanglement due to the spatial degrees of freedom and also the site or local entanglement found in a partition of the potential accessible to measurement. We quantify both using the linear entropy of the reduced density matrix. A sharp variation of the entanglement had been seen in earlier work for the transformation from a one dimensional model core-shell dot to a double dot . We investigate whether the spatial entanglement and energy derivatives display any discontinuity as the core well width becomes small and if the two-electron state is always bound to the core well.