It would take a lot more to implement the derivatives of vectors according to frames.
First, something like '_map_base_scalars' in CoordSys, which would map the base scalars from one system to another.
Something like - 
mapvars = sys1._map_base_scalars(sys2)
somescalar.subs(mapvars)

Thus, 'somescalar', defined in terms of coordinate vars of sys1, would automatically get expressed in sys2.
This could then be used by the relevant methods in vector/ base scalar classes during differentiation.
Since I have already written some code on this, maybe I could help here?