Coherent resonant tunneling through a double quantum dot in an inhomogeneous magnetic field is investigated using a generalized Hubbard model. The conductance is calculated analytically for the case of a single spin-1/2 orbital per dot and numerically for dots containing multiple orbitals using a multi-terminal Breit-Wigner type formula, which allows for the explicit inclusion of inelastic processes. Giant spin-dependent many-body corrections to the transport are predicted to be a clear signature of the formation of a molecular-like state in the system.