OK, I checked your Max file: the model is complex – separate meshes for eyeballs, teeth (upper/low jaws), mouth cavity. There might be problems with correct morph animations of separate meshes in one nif. I tried that in the past and have no good solution. However, this is another story.
For morphing you are using external plugin (Copy-O-Matic or whatever). That’s fine in case you clean your work and use only endogenous Max morpher modifier for the export. So, create both morph targets (snapshot mesh), apply to all three meshes XForm modifier, collapse all for them, then work with morpher as usual. Uncheck “Collapse Transforms” and “Zero Transforms” in export options. This should work. It works for me in Max2010 (I can post exported nif but it is not polished and I did not work with teeth and mouth cavity animations). Max “remembers” all transformations, hence, it is necessary to clean them (XForm). Indeed, NifTools exporter has some problems with animated meshes (their roots), so play with exporter settings (e.g. “Collapse Transforms” and “Zero Transforms”).
I am usually using (prefer) this tutorial by Rhedd:
http://www.tamriel-rebuilt.org/?p=modding_data/tutorials§ion=2867