You draw with

GL.BindVertexArray(mVertexArrayObjectIDs[1]);
GL.DrawElements(PrimitiveType.TriangleFan, 4, DrawElementsType.UnsignedInt, 0);

however the indices you use are for PrimitiveType.Triangles

You draw with

GL.BindVertexArray(mVertexArrayObjectIDs[1]);
GL.DrawElements(PrimitiveType.TriangleFan, 4, DrawElementsType.UnsignedInt, 0);

however the indices you use are for PrimitiveType.Triangles

Replace that with

GL.BindVertexArray(mVertexArrayObjectIDs[1]);
GL.DrawElements(PrimitiveType.Triangles, 6, DrawElementsType.UnsignedInt, 0);