If Robert Moses had his way – and he very nearly did – instead of the Brooklyn Battery Tunnel running under Red Hook to the Battery in lower-Manhattan there would have been a bridge. The bridge was proposed in 1939. Despite strong opposition – arguments against it included that it would destroy historic Castle Clinton at the lower tip of Manhattan, interfere with ship traffic, and mar the harbor view – Moses got the approval from the City and State. Robert Moses was a power broker who held several positions including Chairman of the Triborough Bridge Authority. In the wranging over financing this connector between Brooklyn and Manhattan he also wrested control over the Tunnel Authority.
The bridge, which would have run right along side Red Hook's Atlantic Basin, still needed approval of the War Department, and New Yorkers Elinor and Franklin Roosevelt who were neither fans of the bridge or Robert Moses had the plan nixed.
Instead of a bridge, work on the Brooklyn-Battery Tunnel began in 1940 and was completed ten years later.
Robert Moses had a much greater effect on Red Hook though, then the bridge likely ever would have done with the construction of a network of expressways, a portion of which runs along Hamilton Avenue creating a break between Red Hook and the rest of Brooklyn. The plan which included the Brooklyn-Queens Expressway was proposed in 1936, as an alternative way to improve traffic flow between Brooklyn and Manhattan, instead of the Brooklyn Battery Bridge.
Look in the Sources section below for links to several stories about the Brooklyn-Battery Bridge. The newspapers devoted a lot of ink to the battle of the bridge, two articles as examples are included in the images below.