I assume you've going to see Machu Picchu and also Cuzco. We acclimated at a town at a lower altitude than Cuzco before going to Machu Picchu. Expensive to stay at the Sanctuary Lodge right outside is the park but that gives you the best opportunity to see the place. We hired a wonderful personal guide from Lima. You definitely want a zoom lens that gives you wide angle. After Machu Picchu we boarded an Oceania cruise ship and south. Most of the stops in Cile were lousy. Nothing much to see except Valparaiso. Cruise didn't get good until we got into the starts of Magellan and saw the glaciers. Going further south and around the cape there were interesting countries like Montenegro, Ushuaia, and the Falklands Then to Argentna to photograph Iguazu Falls. I think I used the Nikkor 10-24 DX most of the time there. Buenos Aires is a beautiful city and your 24-70 should be just fine.

My argument is simple advice. If you can easily take it then do so. It is much easier to carry equipment that you wont need than it is to need equipment that you left at home. If you are packing and flying/going by ship or whatever, put stuff in your carryon, your wife's carry on, kid's carryon etc. to get it there. If weight is an issue, leave the wife and take the gear. Another option and this has issues since you are traveling overseas and is not as easy as cross country is to have someone ship the extra stuff to you after you arrive. (doing this overseas gets into tariffs etc. and could be less expensive to purchase while there). Also IF YOU PURCHASE CAMERAS, LENSES etc while overseas, keep a copy of your airline tickets, hotel bill etc. to prove warranty for purchases outside of your home country. Nikon USA requires them for warranty on Non-NikonUSA warranties honored in the US and other camera companies appreciate it as it makes their life and documentation easier.(even if they don't require it).

Well - you do not ay where exactly you will be going and what activities you will be doing - that limits what we can advise. Are you going to the Galapagos? Are you going to the Amazon? Are you going to visit the Sacred Valley or Machu Picchu in Peru?

I think your lens choice needs a little more range - not just for people, for wildlife, and simply to give you more choice in composition. This is a once-in-a lifetime trip. Can you afford a better longer-range zoom?

Other recommendations regarding travel health: Watch some short videos of mine at:
http://www.rainforesteducation.com/about2/travelhealth.htm

Make sure you have had Hepatitis A vaccine (not the more common Hep B vaccine). Also make sure you take along prescription antibiotics useful for traveler's diarrhea. If you will be going into the Amazon basin you will need malaria prophylaxis. Make sure you take insect repellent (I like the DEET wipes - they can be pulled out when needed and are not greasy) and pretreat your clothing with permethrin.

Also - you are required to have a Yellow Fever vaccination - and an international "Yellow Card" documenting that vaccination - to travel from one country to another within the Yellow Fever endemic zone. Regardless of whether or not you will be going into the Amazon, which would be the only place at risk.

Zika is spread by the same mosquito that spreads Dengue Fever, which is present throughout the tropics. Breeds in small bodies of water in towns and cities, and bites in the daytime (as opposed to malaria which is a rural problem from mosquitoes that bite at night-time). No vaccine exists for either Dengue or Zika - neither is likely to kill you but either might make you wish you were dead for a few days. Dengue is nicknamed "breakbone fever" if that is any clue! Again - keep repellant with you and use it liberally whenever you are aware of the presence of mosquitoes!

A cautionary tale: I had a patient who had mentioned he was going to Puerto Rico to visit relatives. A few months later when I saw him I asked how his trip went - he said it was terrible - that he had spent most of it in the hospital. He said he came down with Dengue on the fifth day of his stay! I laughed, and said that he must have set a record, since the incubation period of Dengue is five days - and he said that in fact, the moment he stepped off the airplane at the airport he was swarmed by mosquitoes! He literally was infected minutes after arrival!