Hi Max, 3 days should be ok. You should get an early morning flight to Jiuzhaigou on day 1 and go straight to Huanglong National Park. Then that evening go to Jiuzhaigou and overnight in Jiuzhaigou.
Then on day 2 go into Jiuzhaigou for the full day. On day 3 book a late evening flight if you can and spend day 3 either in the national park (you could do a hiking trip) or you could visit a local home stay and go hiking in traditional villages outside of the national park.

You should book in plenty of time for this period though because it is one of the Chinese national holidays and always very busy - especially the 1st - 5th or so.

To travel from the airport there are shuttle busses that will leave if there are a min of 5 people. This costs 45 RMB per person to Jiuzhaigou or 100 RMB each to Huanglong and then Jiuzhaigou.
A taxi to Jiuzhaigou costs 200 and you will have to bargain to go to Huanglong and then Jiuzhaigou. It could cost between 300 and 500. The drive from the airport to Jiuzhaigou is around 80mins and that's where the hotels are. I would advise against booking a tour inside the park. Pick up some literature at the park entrance and explore yourself.