We study evolution of self-interacting dark matter subhalos in the Milky Way tidal field. The interaction between the subhalos and the Milky Way's tides lead to more diverse dark matter distributions in the inner region, compared to their cold dark matter counterparts. We test this scenario with two Milky Way satellite galaxies, Draco and Fornax, opposite extremes in the inner dark matter content, and find that they can be accommodated within the self-interacting dark matter model proposed to explain the diverse rotation curves of spiral galaxies in the field.