Take flight from Delhi to Dehradun, take bus or cab to Massorie, 1day is sufficient for massoorie then take cab or Bus to Joshimath via Rushikesh it would take approx 10-12hr but u would definitely enjoy the journey.... auli is just 16km from joshimath
Here is the itinerary which you can follow --> Day 1 - Dehradun to Mussoorie & sightseeing ( 35 km Drive, 1 hr approx) Day 2 - Mussoorie to Rudraprayag (180 Km, 6hr approx) Day 3 - Rudraprayag to Joshimath sightseeing and drive to Auli (120 Km, 4 hr approx; 10 km, 30min approx)
Day 4 - Auli sightseeing
Day 5 - Auli to Rishikesh (8-9 hrs)
Day 6 - Rishikesh to Dehradun Drive (1-2 hr) and Fly back (Note-** I'm supposing you are traveling private cab**)