How to travel from Lisbon to Seville and Moorish Hotels in Seville

Hello-we will be ending a tour in Lisbon and wanted to take a few days to head over to Seville. I see there is no direct train route. Has any one done this before? Hire a private transfer? Train to Faro-bus to Seville? Rent a car and drive there? Open to ideas. Also, if anyone stayed in a wonderful Moorish style hotel in Seville-would love to know!