We propose an optimal destination scheduling scheme to improve the physical layer security (PLS) of a power-line communication (PLC) based Internet-of-Things system in the presence of an eavesdropper. We consider a pinhole (PH) architecture for a multi-node PLC network to capture the keyhole effect in PLC. The transmitter-to-PH link is shared between the destinations and an eavesdropper which correlates all end-to-end links. The individual channel gains are assumed to follow independent log-normal statistics. Furthermore, the additive impulsive noise at each node is modeled by an independent Bernoulli-Gaussian process. Exact computable expressions for the average secrecy capacity (ASC) and the probability of intercept (POI) performance over many different networks are derived. Approximate closed-form expressions for the asymptotic ASC and POI are also provided. We find that the asymptotic ASC saturates to a constant level as transmit power increases. We observe that the PH has an adverse effect on the ASC. Although the shared link affects the ASC, it has no effect on the POI. We show that by artificially controlling the impulsive to background noise power ratio and its arrival rate at the receivers, the secrecy performance can be improved.