The combination of digital twins (DT) and heterogeneous vehicular networks (HetVNets) can significantly enhance the resource integration capability and performance of the network. In DT-HetVNets, vehicles need to selectively synchronize the data to be updated or cached to their DTs deployed in the cloud for data interaction and decision-making. However, considering that vehicles have diversified data synchronization requirements and network infrastructures have differentiated access capabilities, how to formulate optimal network access strategies and resource pricing strategies for vehicles and network infrastructures becomes a key challenge in the data synchronization process. To this end, we propose a utility-based on-demand data synchronization scheme in DT-HetVNets. In this scheme, we first establish the DT model and communication model in DT-HetVNets. Then, we design the utility functions of the DTs of vehicles and infrastructures by comprehensively considering their requirements. According to the utility functions, we model the decision-making process between the DTs of vehicles and the DTs of infrastructures as a Stackelberg game, where an iterative algorithm is proposed to obtain the Stackelberg equilibrium. The simulation results show that our scheme can bring them the highest utilities compared with the traditional schemes.