As I understand it, you're flying US -> Istanbul, long wait, Istanbul -> Italy, holiday in Rome, Rome -> Frankfurt, long wait, Frankfurt -> US, and you're looking to exit the airports in Turkey and Germany during your layovers?
There are therefore two questions, one for Turkey, and one for Germany. However, note that the 2nd one is different to most people, but we'll come to that in a minute.
In Turkey, both of you should be able to exit the airport provided you have got a visa beforehand online. Take a look at the Ministry of Foreign Affairs page on Visas for Foreigners page for details, then apply on the official evisa site. (Because your wife has a schengen visa, that makes things much simpler for her than would normally be the case for an Indian citizen). I believe that the visa-on-arrival scheme stopped on April 17, 2013, and you now have to do the e-visa beforehand.
For Germany, the Do I need a transit visa to travel from US to India via Europe question doesn't cover your case, so take care when looking for answers! The actual answer for your case - no additional visa is needed. Your wife has a schengen visa, which she'll use to enter Italy in Rome. After that, she's in Schengen, and can move freely around within the Schengen area until her visa runs out. This means that going from Italy to Germany on a direct flight doesn't need another visa, as it's all part of a single Schengen trip. Thus, when you arrive in Frankfurt from Rome, there won't be a passport check as your trip is within Schengen, and you'll be able to exit the airport. (Had you come from outside Schengen, that would be a different matter, see the other question for details on that)