How old are your wife's aunts? Measles is relatively mild virus for children but very dangerous for adults. You are lucky as measles can cause blindness in adults. Someone in your position should be sure that you and your family have the vaccines that are available today. There is a common three way called MMR (measles, mumps, rubella) which you should certainly have your daughter get as soon as she is old enough. I know these are available in Vietnam because they are required for emigration to most western countries. When I was young, these vaccines did not exist and parents like mine used to send their children to the homes of those who had them to get them and be done with it. There are vaccines for whooping cough and chicken pox (varicella) now too. Chicken pox is common enough to have a specialty hospital in HCMC just for that, yet the disease is very preventable. Polio has been eradicated from Vietnam but still exists in Pakistan so one could take a wait and see on that one. If you go to a western type clinic they should identify what you need. One other thing you could do is see what your vaccines are advised by your country for travel in Vietnam. It is rather odd that use of these vaccines is not more widespread as they are well within the means of most city residents, who will spend way more for toys than these vaccines cost. For the nation, the losses from viral diseases can far outweigh the costs of vaccination. The "Socialist" Republic really needs to expend the resources. I know Vietnam has worked on Polio and of course Malaria but they could tackle a few more.
As far as bacterial diseases, my personal philosophy is to build natural immunity through reasonable exposure. When my daughter finished the 6th grade, I was surprised that she was recognized as the only child who had finished all 6 years with perfect attendance. In hindsight I attributed her wellness to the fact that we had a swine farm at that time and her exposure made her healthy. My Canadian mother used to say "You eat a peck of dirt in your lifetime." You don't want to teach your daughter to swim in Song Sai Gon, but don't worry too much.
Your observation about the doctor asking your wife about a fever is typical and shows up what I think is the weak link in Vietnamese medicine which is first line diagnosis. In three years, I never had a doctor take my temperature or blood pressure but they did ask me how it was.
I also had a doctor misdiagnose shingles (benh zona) as a bacterial infection and give me the overly used antibiotics which were of no use. Luckily, a second doctor did recognize it for what it was. Another weak link is record keeping. Doctors expect patients to keep the records which of course fails to happen.
I taught a home class of doctors for a while, which gave me some insight. The curriculum that I found. developed by a physician teaching doctors in the Czech Republic, was heavy on role playing of patient interviews which is the main point of interaction for doctors dealing with foreign patients. I immediately noticed that my doctor students would try to shortcut the interview with a quick diagnosis. This may be a habit they develop in the overcrowded clinics but it can lead to incorrect diagnosis. They never ask about family history which can be critical. Maybe this is based on a cultural reluctance to ask. Either way, both as a teacher and as a patient, I found Vietnamese doctors too quick to arrive at a diagnosis.