Topological photonic crystals with robust pseudo-spin and valley edge states have shown promising and wide applications in topological waveguides, lasers, and antennas. However, the limited bandwidth and intrinsic coupling properties of a single pseudo-spin or valley edge state have imposed restrictions on their multifunctional applications in integrated photonic circuits. Here, we propose a topological photonic crystal that can support pseudo-spin and valley edge states simultaneously in a single waveguiding channel, which effectively broadens the bandwidth and enables a multipath routing solution for terahertz information processing and broadcasting. We show that distorted Kekulé lattices can open two types of bandgaps with different topological properties simultaneously by molding the inter- and intra-unit cell coupling of the tight-binding model. The distinct topological origins of the edge states provide versatile signal routing paths toward free space radiation or on-chip self-localized edge modes by virtue of their intrinsic coupling properties. Such a powerful platform could function as an integrated photonic chip with capabilities of broadband on-chip signal processing and distributions that will especially benefit terahertz wireless communications.