Hi Kevin,
it is not 100% clear what you want to do but most likely you will need to write your own code for this. One thing that you might want to use: if you want to know in which coarse triangle the vertices of the finer mesh are, you can use InterpFromMeshToMesh2d and interpolate the "number" of the coarse elements onto the finer one:
coarseID = InterpFromMeshToMesh2d(coarse_index,coarse_x,coarse_y,1,fine_x,fine_y);
The vertex number "i" of the fine mesh is in the triangle coarseID(i) of the coarser mesh.
If you see that for one triangle of the fine mesh, the coarseID of all the vertices of this triangle are the same, that means the the triangle is entirely included in a bigger triangle.
You can use coarseID(md.mesh.elements) to get the table of the coarse elements in which the 3 vertices of the finer triangles are.
Best,
Mathieu