Ho Chi Minh is a very crowded city. Unless you plan to taking sniper people shots, don't bring the 80-200. And honestly... the 80-200 is NOT too heavy. If it's too heavy for you to the point where you don't want to bring it along for travels, then why did you buy it? You hsould have just gotten a cheap and light sigma 75-300.
It depends heavily on what you intend to shoot while there, and also whether you are willing to sacrifice lens speed for traveling light. There will be no uniformity in answer, Everyone has their own opinion on their preferences.
I used to think my ( 70-200 ) was too heavy and bought an 18-200mm for my usual holidays. Until recently i finally brought it out for a spin in Japan. And realized what shooting joy I missed. It is not really heavy actually.
If u already excluded the 80-200mm and yet you need the longer focal length, a lightweight option would be to just rent an 18-200 and be on the go. Alternatively you can also bring your 18-35 and the 35/2 or even either of them alone as well but prepare to miss abit at the longer end
Yeah, I'd agree with bringing the 18-35mm and extra batteries. I'd usually bring along my charger just in case, plus do take note of the type of sockets they use overseas. I bought a 18-200 VR for travelling and had no regrets, leaving it on the body most of the time.