I would suggest staying at the Westin Osaka (taking a guess with your SPG Plat status).
If you need that extra stay. You can move to Sheraton Miyako Osaka on the day you go to Nara. Take your bags on the underground or take a taxi (might cost 2000-3000yen from Westin Hotel) and leave your bags at the hotel before you head out to Nara.
Go explore Kyoto on the first day. Second day around Osaka. Third day Nara...