The number of hops from Mesh Routers (MRs) to an Internet gateway (IGW) plays an important role in determining the performance of a wireless mesh network (WMN). A recent patent has introduced a mechanism of using an existing femtocell (FC) as an additional potential IGW so that the performance of a WMN could be enhanced. Such an integration of WMN with FCs enables an increase in WMN's overall capacity. But, due to FCs' unpredictable operating times and uninformed disconnections, MRs require reliable and efficient schedule for switching between available FCs which has not been analyzed in the patent. The switching can be done in a push based preemptive or a pull based non-preemptive manner. In this paper, we formulate both these switching schemes for a WMN-FC integrated network as approximate statistical models based on a Markovian process. We also determine a switching schedule of FCs for each of MR based on reliable uncapacitated facility location (RUFL) problem. We extend an existing RUFL problem to incorporate dynamic operating nature of multiple FCs which display dynamic available/unavailable patterns for additional potential IGWs. Extensive simulations are carried out to validate our proposed statistical models and establish the performance of these switching schemes.