Free trade is going to be far more effective in changing Cuba and Iran than sanctions were.
This is quite true. There is proof that free trade makes nations less likely to go to war. First, protectionist policies, tariffs, dumping, and the like can create retaliatory protectionist policies by other nations. Nation A then retaliates trade wise with Nation B, who then retaliates back, diplomacy and negotiation break down and cooler heads may not prevail. Indeed, World War One, and many other wars that preceded it, could be traced back to hostility that arose from tariffs and other trade barriers.
Second, free trade creates an intermingling of economies and a (to quote Keohane and Nye) "complex interdependence." To illustrate this, pretend that nation A relies on nation B for its cars, on nation C for its computers, one nation D for its steel, and on nation E for its wheat (and nations B,C,D, and E on one another for various goods). As a result, Nation A is not likely to bomb the shit out of any of these states as it will then have to spend more money to buy the goods/resources from another country, or settle for a lower quality good/resources. Not to mention the fact that if, say, country E got the shit bombed out of it, then it won't produce wheat. Thus, the price of wheat will go up on the international market, exacerbating negative effect to Country A (it has to buy from a more expensive nation and with decreased supply and similar demand, the price will naturally skyrocket). The end result is that it's a form of mutually assured destruction (or mutually assured inconvenience) for Nation A to bomb the shit out of one of these Nations since Nation A and its citizens will then lose access to the cheaper and higher-quality goods/resources that nation produced.
Quite frankly US foreign relations are more complicated than 'looking into bullshit'. The US will always be criticised for either being too isolationist or too interventionist.
This is also an astute observation. America is the single superpower militaristically in the world and the most powerful economy in the world. As such, when shit goes down in a random country, there are often cries among that country and the international community for us to step in and do something (either through money or through military). The Honduran situation that I brought up is a good example: America did its best to sit its happy ass out of it, and one person in Honduras literally and specifically called out Hillary for not stepping into protect the democratically elected government (before the new military-government assassinated her). On some level, I think humans have a moral obligation to step up and prevent genocide--especially after what we witnessed during the genocide-happy 20th century. But that doesn't mean we should get involved in every conflict, nor does that justify any action we take, nor does it give us a pass to Bush style nation building. International policies are a complex situation and easy, correct answers are very hard to come by.
