We report on experimental and theoretical investigation of mode-splitting dynamics in a ring cavity under the perturbation of fractional Bragg reflection from a periodically-poled nonlinear crystal. Counterintuitively, pronounced mode splitting in the spectral domain could have been observed even with a tiny intensity reflection of 0.0003. The breaking of running-wave operation in the ring-cavity configuration resulted in comparable circulating fields in forward- and counter-propagation directions, which thus dramatically reduced the enhancing factor for the resonating field. In contrast, a linear cavity with intrinsically bidirectional operation was immune to the small intra-cavity reflection. Therefore, the linear-cavity layout could provide an expedient solution for a given internal reflection to obtain more stable and higher enhancement, which was confirmed by comparative studies of mid-infrared generation based on pump-enhanced difference frequency conversion. The underlying mechanism was further modeled by numerical simulations, which agreed well with experimental results. These findings could not only shed light on the understanding of the exotic feature of concatenated optical cavities, but also provide a useful guide to practical design of enhancement cavities for cavity-based frequency conversion with periodically-poled nonlinear crystals.