There's no reason why we can't put conditions on trade. We can draw the line as a country and decide that we won't do business OR we will impose a severe penalty on those who do to take away the financial incentive to continue the practice. The problem is, it will take more than the U.S. government doing this. Everybody will need to stand firm together for it to actually work, and there's a large uphill battle for that to happen.
While banning products made by children will force some large factories in countries such as China and Bangladesh to ease back on staffing their operations with children, it is likely that smaller enterprises will ignore the restrictions. Many families in areas such as rural India are reliant on children for support and the children will not stop working. Poor oversight of the providence of these products will ensure that they will keep making their way to America.
Unfortunately I do not believe that any ban against imports of child slavery goods will affect child slavery at all. The ban from a single country would certainly not help if other countries do not unite against it. The issue remains the economic trouble of those countries that allow such acts to be committed in the first place and they will always find a loophole to continue on their venture.
It is true that the United States is a very powerful country in this world, and indeed, a lot of other countries' economies and livelihoods depend on the United States citizens to buy their goods. However, just because the United States has stopped purchasing goods made from child slavery, it does not follow that all countries will cease to use child labor for production. It may greatly be reduced, but not stopped. Instead, some child labor will go under ground, but continue. Some businesses will actually become legitimate, and hire the children at a pittance of a salary. Some businesses may go so far as actually stop using children, but they will be unable to compete in terms of price. Regardless, the United States' actions alone will not be enough to completely stop child slavery.