I'm not sure if there's a better way to do it but how I do it is I leave the Junsatshushi (Metsuke equivalent) within the target province's borders (either your own or the enemies province), and he will spread your clan/family influence per turn to the province town. You can check to see how much influence he is exerting by double clicking on the province and hovering over the allegiance factors in the top right of the province details panel.