Constrained Delaunay with Info - cgal

Question

I have this setup:
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Triangulation_vertex_base_with_info_2<FIntPoint, K> Vb;
typedef CGAL::Constrained_triangulation_face_base_2<K> Fb;
typedef CGAL::Triangulation_data_structure_2<Vb, Fb> Tds;
typedef CGAL::Exact_predicates_tag Itag;
typedef CGAL::Constrained_Delaunay_triangulation_2<K, Tds, Itag> Delaunay;
typedef Delaunay::Point Point;
typedef Delaunay::Vertex_handle VertexHandle;
FIntPoint is a struct with 2 integers.
My vertices belong to border triangles of 2 separate terrain-like 3D meshes. I triangulate these vertices in 2D to connect these meshes. The info I need for each vertex is (1) which mesh it belongs to and (2) its vertex index within that mesh, so that I know where this vertex came from after triangulation, as more information is tied to these indices.
In this illustration, you can see the 2 meshes and their border triangles. I want to stitch these together:
This is basically how I insert points, simplified:
Delaunay Triangulation;
for (...)
{
// Insert a triangle from one of my meshes
VertexHandle vh1 = Triangulation.insert(Point(a.Y, a.Z));
vh1->info() = FIntPoint(iA, iM);
VertexHandle vh2 = Triangulation.insert(Point(b.Y, b.Z));
vh2->info() = FIntPoint(iB, iM);
VertexHandle vh3 = Triangulation.insert(Point(c.Y, c.Z));
vh3->info() = FIntPoint(iC, iM);
// Add constraints to keep this triangle exactly how it was in the origin mesh
Triangulation.insert_constraint(vh1, vh2);
Triangulation.insert_constraint(vh2, vh3);
Triangulation.insert_constraint(vh3, vh1);
}
My problem now is that when I try to retrieve the info, it is missing/incorrect. I get values outside of the range I'm inserting them.
This happens only with the constraints. When I comment out the lines with insert_constraint, it works as expected.
for (auto itFace = Triangulation.finite_faces_begin(); itFace != Triangulation.finite_faces_end(); itFace++)
{
// Retrieve vertex info
auto& a = itFace->vertex(0)->info();
auto& b = itFace->vertex(1)->info();
auto& c = itFace->vertex(2)->info();
// ...
}
What am I doing wrong with the constraints?
Additionally, I want to limit the length of edges. I haven't attempted so add this limitation in my code yet, because I wanted to fix the described problem first. If you could provide an answer that includes a maximum edge length, that would be very helpful too.
Any help is appreciated. I've been sitting on this problem for a long time.