The triangle of the three desert kingdoms are Bikaner, Jodhpur and Jaisalmer.
 

Day 1: Arrive in Jaipur. Sightseeing at Amber and the Pink City, including an elephant ride.
Day 2: After breakfast, drive via Samode with its lovely palaces, through the painted towns of Shekhwati to Mandawa for overnight at the castle.
Day 3: Sightseeing at Mandawa, and then depart for Bikaner with picnic lunch.
Day 4: Sightseeing of fort and museums of Bikaner and depart for Jaisalmer.
Day 5: Sightseeing of Jaisalmer fort and temples. After lunch, drive to Jodhpur.
Day 6: Sightseeing at Jodhpur and nearby Mandore. Tour ends with evening flight to Delhi/Mumbai (In a variation of this trip, you can eliminate Bikaner. and replace it with the small desert village of Khimsar where the fortified palace is a heritage hotel.)