모시다 is the honorific verb for looking after someone — driving them, escorting them, having them as a guest — and it lowers the speaker relative to the person served. 안전하게 모시겠습니다 ('I'll get you there safely') appears three times, which is exactly what a driver or a service says to a passenger. 힘들게 모신 거라니까 and 어렵게 모심 mean it took real effort to get the guest to come at all.