This work establishes the diversity-multiplexing tradeoff (DMT) of the four-phase decode-and-forward (DF) protocol in the half-duplex, non-separated two-way relay channel. We consider a fading channel model where the source relay links are Rayleigh distributed but the direct link between sources is left more general as Nakagami-m distributed and investigate for any possible gains in the achievable DMT using four-phase hybrid broadcast (HBC) protocol, as compared to three-phase time-division broadcast (TDBC) protocol. For the statistically symmetric case of Rayleigh fading and asymmetric fading with more stable direct link (m > 1), the optimal DMT of the HBC protocol is computed and is shown to be achieved by a three-phase orthogonal variant, TDBC protocol. The operational meaning of this result is that the multiple access channel (MAC) phase of HBC protocol is not necessary to achieve optimal performance, this results in a simplification of the communication protocol. For less stable direct link (1/2 ≤ m < 1), the analysis establishes that the MAC phase of HBC protocol is necessary to achieve optimal DMT. {\textcopyright} 2011 IEEE.