The BGO calorimeter of the Canadian $8\ensuremath{\pi}$ $\ensuremath{\gamma}$-ray spectrometer was used to select the weak $2p$ channel in Ni-Ni fusion reactions, populating proton-rich ${}^{114}\mathrm{Xe}$ and ${}^{116}\mathrm{Xe}.$ Lifetimes were measured for transitions within the low-lying positive and negative parity bands in ${}^{114,116}\mathrm{Xe}.$ Measured $B(E2)$ values within the positive parity band were compared to calculations with algebraic models. Measured $B(E2)$ values within the negative parity band in ${}^{114}\mathrm{Xe}$ suggest a change in structure relative to that of the same band in the heavier xenon isotopes.