Experiments by Poulard and Cazabat [Langmuir 21, 6270 (2005)] on spreading droplets of nematic liquid crystal (NLC) reveal a surprisingly rich variety of behavior, including at least two different emerging length scales resulting from a contact line instability. In earlier work [Cummings, Lin, and Kondic, Phys. Fluids 23, 043102 (2011)] we modified a lubrication model for NLCs due to Ben Amar and Cummings [Phys. Fluids 13, 1160 (2001)] and showed that, in a qualitative sense, it can account for two-dimensional (2D) versions of the observed behavior. In the present work we propose a different approach that allows us to explore the effect of anchoring variations on the substrate, again in a 2D geometry. This in turn gives a simple way to model the presence of defects, which are nearly always present in such flows. The present model leads to additional terms in the governing equation. We explore the influence of these additional terms for some simple flow scenarios to gain insight into their influence.