We show that, in appropriate regimes, ultracold collisionally shielded molecules in an optical lattice realize a controlled extended Hubbard model, despite their large-radius hard-core repulsion. We compute the Hubbard parameters and show lattice depth and microwave-induced dipolar interactions provide flexible, independent control of on- and off-site interactions. This makes shielded molecules a powerful platform for extended Hubbard models and enables an interaction microscope that can distinguish inter-hole interactions in doped Mott insulators - crucial to superconductivity and strange metallicity - that are indistinguishable with quantum gas microscopy alone.