  We explore the response of an unconventional superconductor to spatially
inhomogeneous antiferromagnetism (SIAFM). Symmetry allows the superconducting
order parameter in the E-representation models for UPt3 to couple directly to
the AFM order parameter. The Ginzburg-Landau equations for coupled
superconductivity and SIAFM are solved numerically for two possible SIAFM
configurations: (I) abutting antiferromagnetic domains of uniform size, and
(II) quenched random disorder of `nanodomains' in a uniform AFM background. We
discuss the contributions to the free energy, specific heat, and order
parameter for these models. Neither model provides a satisfactory account of
experiment, but results from the two models differ significantly. Our results
demonstrate that the response of an E_{2u} superconductor to SIAFM is strongly
dependent on the spatial dependence of AFM order; no conclusion can be drawn
regarding the compatibility of E_{2u} superconductivity with UPt3 that is
independent of assumptions on the spatial dependence of AFM
