Due to their Radio-Frequency (RF) immunity, Visible Light Communications (VLC) pose as a promising technology for interference sensitive applications such as medical data networks. In this paper, we investigate mixed RF-VLC relaying systems especially suited for this type of applications that support mobility. In this system setup, the end-user, who is assumed to be on a vehicle that is in dynamic movement, is served by an indoor VLC system, while the outdoor data traffic is conveyed through multiple backhaul RF links. Furthermore, it is assumed that a single backhaul RF link is activated by the mobile relay and due to feedback delay, the RF link activation is based on outdated channel state information (CSI). The performance of this system is analyzed in terms of outage probability and bit error rate (BER), and novel closed form analytical expressions are provided. Furthermore, the analysis is extended for the case where the average SNR over the RF links and/or LED optical power is high, and approximate analytical expressions are derived which determine performance floors. Numerical results are provided which demonstrate that the utilization of multiple RF backhaul links can significantly improve overall RF-VLC system performance when outage/BER floors are avoided. This calls upon joint design of both subsystems. Additionally, the outdated CSI exploited for active RF selection can significantly degrade the quality of system performance.