Hello E & J,
Yes indeed you can do all of this in two weeks, but bear in mind that Argentina is a huge country, through definately easier to travel than Peru.
Forget trains. Regrettably they are a thing of the past. The saddest thing is to see Retiro Station in Buenos Aires. Many years ago I had left Buenos Aires by international train to Peru, a 5-day epic journey. In those days, the magnificent Retiro Station had been thronged by crowds travelling to all parts of Argentina and the neighbouring countries of Chile, Paraguay, Brazil, and Bolivia. Now it is a shadow of itself. The bustling platforms are empty and the elegant restaurants and shops abandoned. The three impressive railway stations standing side by side now just serve suburban traffic, and bustle only at morning and afternoon rush hours. Sad, but that's progress.
Now the way to travel is by air (expensive) and by bus
(inexpensive). We travelled on the luxury overnight bus to Mendoza from BA. Here was our experience:
"At the bus station we are directed to the platform our vehicle will be leaving from. The modern double-decker looks impressive and we ascend the stairs to the upper floor. We sink into our commodious seats. Surely no airline seat even faintly resembles this. We try out the reclining system and find it lies back fully to make a flat bed."
"The motor coach leaves exactly on time. Shortly afterwards our hot dinner arrives, not exactly gourmet, but of sufficient quantity and quality to satisfy. It's even served with wine, though judging by the taste, it is pure plonk, but certainly good enough for getting you drowsy."
"The DVD movie is not working well, so with such comfort, we are all soon sound asleep."
These buses run all over Argentina. From Mendoza its a long 17-hour run along the foothills of the Andes to Bariloche. Nevertheless it's a very scenic route and a very comfortable bus.
You probably want to see Valdes Peninsular. Bus from Bariloche to Trelew or Puerto Madryn to visit this amazing wildlife area, then bus from there to El Calafate for the Perito Moreno glacier.
You are now so far south that the bus back to BA would be a killer, so spring for a one-way airfare in this case back to BA.
With all this, you should still have time for a day on the pampas and a trip by ferry to Uruguay.