Not sure where your fiance or wife is from, but in Hanoi this process is very fast. Maybe I can give a little more detail as to what you need exactly. First visit So Thu Phap in Ha Dong 1B Tran Phu Street. The list you get says you will need a single status paper, which I got directly from the US Embassy($50) and brought straight to Vietnamese Consular at 40 Tran Phu in Ba Dinh to have it verified. It takes one day and cost 30,000vnd. You are correct you need a Medical check at a certified hospital, So Thu Phap will give you a list of the closest hospitals to your home. We didn't book an appointment or anything, just asked about what time they are available to do the check up and went there right away. If you do it in the morning you can have the paper back that afternoon, we did it on a Friday and had to wait until Monday to get the paper back. Then you need to bring your passport to a translation office, I used one near Vincom, it took one day to complete. That is it. It will take 15 days to process your paperwork after turning it in to So Thu Phap then you go there as a couple for some questions, then the paperwork states you must show up right away when they finalize the papers normally takes 10 more days. If she is from Hanoi she will only need to show her ID, single status which takes a day from her Districts Ward, the health paper, and family house book, will not need to get any police checks. Follow the instructions and do everything they ask and at the most it should take one month. Don't listen to these guys and worry that it is something that will take 6 months or 1 year or it is impossible. As for the kid, register him or her at your embassy and they will be your nationality.
Also if you get your single status paper from the US Embassy it is in Vietnamese and will not need to be translated. Only have the stamp verified at the consular.
Update : Turned in all the papers at So Thu Phap this morning, the initial instructions said I would have to wait 10 to 15 days to get an appointment for our interview. But we have our interview Monday at 2pm. Anyone know what kind of things are asked in these interviews?? One thing, they are making us use their translator at some small fee, since I can't speak enough Vietnamese to talk and answer. So the actual time I have invested in this is about 1 hour of filling out forms, a visit to the doctor and waiting the weekend for the report. A visit to the US Embassy for my single status and a one day wait to have it verified by the Vietnam Consulate. They didn't even take my translated passport, they just photocopied my information page and visa with the stamp.