An american citizen “interning” in Sweden, but was just using the 90 days period for this intern period. However I have a family event in Italy on the 92nd day of my stay and would like to stay 2 more weeks in Italy- what are my options to extend my visit without getting into trouble - I want to depart from Italy back to the states, but I came through Sweden.
Your only options for doing this legally are:
Somehow get a long-stay visa for Sweden that will cover some of your days there. This will exempt those days from the Schengen clock. However, I don't know if you have time for that, or even if Sweden would be willing to issue a long-stay visa to someone in your situation.
Leave the Schengen area for at least two full days, such that you will have enough time on your Schengen clock to be present in the area on the "92nd day". Get a Monday off and spend a long weekend in London, perhaps? Two more weeks sound out of the question.
In the absence force majeure (such as hospitalization, natural disasters, major strikes or the like which physically prevent you from leaving the Schengen area in time), there is no way to "extend" the 90-day limit for short stays.