Customizing CGAL Kernel with my own Point class

Question

I would like to use a custom Point class with the CGAL constrained delaunay triangulation. However, with the following MyPoint class (which should behave the exact same as a CGAL::Point_2 no?) I get segmentation faults. It works perfectly if I set the Point_2 typedef inside MyKernel to CGAL::Exact_predicates_inexact_constructions_kernel::Point_2. What am I doing wrong?

template<class P>
struct MyPoint : public P {
    MyPoint() : P() {}
    MyPoint(const MyPoint& p) : P(p) {}

    MyPoint( int x, int y) : P(x,y) {}
    MyPoint( double x, double y) : P(x,y) {}
};

struct MyKernel : CGAL::Exact_predicates_inexact_constructions_kernel {
    typedef MyPoint<CGAL::Exact_predicates_inexact_constructions_kernel::Point_2> Point_2;
};

typedef MyKernel K;

typedef CGAL::Triangulation_vertex_base_2<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> CDT;
typedef CDT::Point          Point;

Code which segfaults at last line:

CDT cdt;
Point cgal_p1;
Point cgal_p2;
cgal_p1 = Point(p1[1],p1[2]);
cgal_p2 = Point(p2[1],p2[2]);
cdt.insert_constraint(cgal_p1,
                      cgal_p2);