Sandra, I see that you are receiving some helpful tips but that you are also a bit more confused with so many choices at your disposal. Please keep this in mind when making your trip.
Chengdu, Sichuan is a huge city and a great place and has lots to see but it is very different from Yunnan in many ways. Personally, I would just stay in Yunnan as Chengdu has a completely different atmosphere and history and that portion of your trip will only take time from your itinerary that can be better served in Yunnan.
Also, I feel you may be trading one UNESCO site for another.
www.gokunming.com/en/forums/thread/9948/unesco_sites_in_china
I have visited both Emei and Leshan because I am in the process of visiting all 48 UNESCO sites in China. Keep in mind that UNESCO sites in China are very expensive and crowded with tourists all year round.
To answer your question directly, you need a full day to visit each site because of the driving time (distance) and time required to see each site. If you attempt to visit 2 places in one day you will spend a lot of money and cheat yourself out of the travel experience. Leshan and Emei are 86 km apart (2.5 hours).
Pandas - en.wikipedia.org/wiki/Sichuan_Giant_Panda_Sanctuaries - There are several to choose from so this depends on which you will visit.
en.wikipedia.org/wiki/Sichuan - See the map to understand the distance.
I recommend you stay in Yunnan for your entire trip if you have not already purchased tickets and try to see as much as you can in Yunnan.
On a personal note, I can understand why some people may speak negatively of Dali and Lijiang. I have been in Yunnan for 12 years and I have seen the many (FAKE) changes that have taken place and it really makes me feel sad. However, the first time I went to Dali I feel in love with the 1000 year old city and I purchased a home there because the people and the landscape is wonderful.
If you have any questions feel free to send me a PM, I can send you some pictures if needed. Good luck.