That would be under another law not anti-trust which deals with monopolies. When you look at the success of statutes against communist countries or dictatorships it varies depending on the products of that country. There are plenty of Cuban cigars being smoked in the US. How they got here is a mystery....
There has always been trade with dictators and communist countries if it was felt that it was in the best interests of the US. Quite often those interests aligned with certain business interests. Oh and it wasn't always about oil, remember United Fruit Co?
I agree with you on the third party but will there ever be enough voters willing to support a dark horse? Too often we vote "strategically", i.e., we vote someone out as opposed to voting them in.
As for dealing with the robber barons, for the most part, they were reined in by anti-trust laws, child labor laws, work condition regulations, etc..., many of the things that people are railing against today.
Free trade was driven by the US to open up new markets to US companies. What most countries do is create barriers to their markets by either imposing a tariff or forcing companies to situate plants within the countries boundaries thereby benefiting the local population with jobs and local areas with revenues through taxes. The US wanted to do away with such requirements and thus pursued free trade agreements with its largest trading partners.
It is not so much free trade that undermines the economy as it is the nature of publicly traded companies. They have only one master, the shareholder, to heed. Now if they were to have to function to the benefit of "stakeholders" that would alter the approach radically. Stakeholders are generally considered to be, investors(shareholders), customers, employees, municipalities in which the company conducts it's business, suppliers, etc... All of these groups have an interest in how the company conducts it's business and are impacted both good and bad by their decisions.
While we can rail against the current arrangement, it will fall on deaf ears until we can propose a better system.