The volume of video traffic as infotainment service over vehicular ad hoc network (VANET) has rapidly increased for past few years. Providing video streaming as VANET infotainment service is very challenging because of high mobility and heterogeneity of vehicular networks. While the number of mobile gateways (vehicles connected to the Internet) needs to be minimized to reduce service cost, the streaming quality also needs to be satisfactory for end-users. Existing works either focus on gateway minimization or focus on enhancing user satisfaction. We propose a video streaming solution, namely, DGSVS, which does gateway minimization with the constrained time data delivery to end-users. We formulate our constrained gateway minimization problem as minimum set covering (MSC) problem and solve with a distributed approximation method for MSC. We assume that only a subset of vehicles in VANET run DGSVS application. Therefore, instead of application layer cooperation for gateway-client association, network layer cooperation is proposed. We propose a novel multicast protocol DSS-CAST for this purpose, which is specialized in streaming data distribution for dynamic scenarios. We compare the performance of DGSVS with other existing protocols and found that DGSVS is most effective in service cost minimization while it is able to achieve competitive QoE performance.