Software-defined satellite-ground integrated vehicular networks have emerged as indispensable infrastructures that provide rural area coverage and diverse vehicular services. However, previous research on control domain division mostly focuses on data center networks. To address these issues, we formulate the dynamical control domain division (DCDD) problem to minimize the total management cost. Since the DCDD problem is NP-hard, we propose an approximation algorithm RDCA based on the randomized rounding. We formally analyze the performance of the RDCA algorithm. Guided by the rounding procedure, we propose a heuristic algorithm HCA to greedily choose the best controller at each time slot. Two kinds of switch migration operations are designed to further minimize the total management cost. Extensive simulations show that our HCA algorithm outperforms related schemes in terms of management cost, response time and controller load balancing.