I think the key overall point to make is this:
You can think of funny situations where one nations total GDP goes down from an increase in free trade. But, in the vast majority of real world situations, free trade will increase the total GDP of both sides -- and often tremendously over the long run.
But the free trade agreement will sometimes have to be intelligently constructed, and it's important to have some good key local laws and institutions in both countries to make the free trade work well. It's important to realize that with free trade there will be losers in each country, but in each country, in the vast majority of cases, the gainers gains will outweigh the losers losses – and often by a huge amount.
This will especially be true if you have the agreement well constructed and with good supplementary local laws and institutions. But usually, even if you don't, trade will do a lot more good than harm. The main reasons are it allows for greater economies of scale, efficient specialization, greater competition, and less corruption.
Now the last two don't have to result from free trade. You can think of situations where the opposite will happen, but in the real world, it's more likely than not that freer trade will lead to more competition and less corruption. But this is precisely where the side agreements, local laws and institutions are so important – for example, smart anti-trust law with good enforcement.
It is also important to redistribute some of the gains of the gainers to the losers. The gainers gains almost always will outweigh the losers losses, so you can give some of their gains to the losers so that no one loses and everyone gains. This will also increase support for free trade, and make it more likely. Of course, try explaining this to today's Republican party, which believes that thinking beyond simple sound-bites is liberal and un-American.
An excellent case in point is Mexico. Total GDP has increased substantially due to a great increase in free trade, but the income of the vast majority who are poor has hardly increased. Almost all of the gains from free trade have gone to the wealthy. If Mexico had much more progressive taxes, as it should, it could be taxing those gains and using them to invest in education, infrastructure, public health, etc. for the vast majority. This would make essentially everyone gain from free trade, and these high return public investments would make the country much wealthier over the long run.
Dani, I think it's important to stress these things, along with the legitimate criticisms of free trade that you make. I know you make these criticisms not because you're against free trade overall, but because you want to make it better, with better constructed agreements and supplementary laws and institutions. But without stressing at the end that you think free trade is good overall, you risk doing a lot to help those who are fervently against it, and want extreme protectionism, which would hurt every country and devastate the poorest.