Just came back from my Vietnam trip and my itinerary was HCMC, Da Nang/Hoi An, Hue, Hanoi. I took the plane between SGN-DAD, train between DAD-HUI, and plane between HUI-HAN. I don't recommend the train between DAD-HUI unless you're a backpacker. Instead, take a look at some tour companies in either Da Nang/Hoi An/Hue and see if any of them will do a one-way car ride for you.
Personally, I would also cut the # of days in HCMC and put it towards Da Nang/Hue/Hoi An. For Hue, you can do a one-day tour to cover the more popular attractions.