We present observations made with the Berkeley-Illinois-Maryland Association millimeter array of the H2S 2(2, 0) --> 2( 1, 1) and (CO)-O-18 2 --> 1 transitions toward a sample of four hot molecular cores associated with ultracompact H II regions: G9.62+0.19, G10.47+0.03, G29.96 - 0.02, and G31.41+0.31. The angular resolution varies from 1."5 to 2."4, corresponding to scales of similar to 0.06 pc at the distance of these sources. High-velocity wings characteristic of molecular outflows are detected toward all four sources in the H2S line. In two cases ( G29.96 and G31.41) red- and blueshifted lobes are clearly defined and spatially separate, indicating that the flows are collimated. We also confirm the previous detection of the outflow in G9.62F. Although the gas-phase H2S abundance is not well constrained, assuming a value of 10(-7) yields lower limits to total outflow masses of similar to8 M-., values that are consistent with the driving sources being massive protostars. Linear velocity gradients are detected in both (CO)-O-18 and H2S across G9.62, G29.96, and, to a lesser extent, G31.41. These gradients are observed to be at a different position angle to the outflow in G9.62F and G29.96, suggestive of a rotation signature in these two hot cores. Our observations show that these hot cores contain embedded massive protostellar objects that are driving bipolar outflows. Furthermore, the lack of strong centimeter-wave emission toward the outflow centers in G29.96 and G31.41 indicates that the outflow phase begins prior to the formation of a detectable ultracompact H II region.