Running your new plugin I observe that the Powell-Sabin mesh is correct, but there is some difficulty:
When solving the Stokes linear system it takes 6 times more in cpu to get the solution. This indicates a stiff problem.
I think that making the computations of the intersection between the edge and the line joining the two triangle centers in C++ is not accurate enough compared to the same computation in FreeFem++ (that I did).
The consequence is that the points are not accurately enough aligned.
I had such problems before when saving my mesh into mesh1.msh:
I had to indicate a large number of digits when writing into the file.
Is it possible to use higher accuracy in your splitmesh6.cpp script ?
Francois.