We present measurements of the top quark mass (${m}_{t}$) in $t\overline{t}$ candidate events with two final state leptons using $1\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected by the D0 experiment. Our data sample is selected by requiring two fully identified leptons or by relaxing one lepton requirement to an isolated track if at least one jet is tagged as a $b$ jet. The top quark mass is extracted after reconstructing the event kinematics under the $t\overline{t}$ hypothesis using two methods. In the first method, we integrate over expected neutrino rapidity distributions, and in the second we calculate a weight for the possible top quark masses based on the observed particle momenta and the known parton distribution functions. We analyze 83 candidate events in the data and obtain ${m}_{t}=176.2\ifmmode\pm\else\textpm\fi{}4.8(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}2.1(\mathrm{sys})\text{ }\text{ }\mathrm{GeV}$ and ${m}_{t}=173.2\ifmmode\pm\else\textpm\fi{}4.9(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}2.0(\mathrm{sys})\text{ }\text{ }\mathrm{GeV}$ for the two methods, respectively. Accounting for correlations between the two methods, we combine the measurements to obtain ${m}_{t}=174.7\ifmmode\pm\else\textpm\fi{}4.4(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}2.0(\mathrm{sys})\text{ }\text{ }\mathrm{GeV}$.