The rest of the people in the neighborhood will lose their jobs because the house of cheap labor will start doing everything else including plumbing, like carpentry, shoe making, everything.

Well, then you've well beyond your analogy, and into a general broadside against international trade. As a general matter, I believe that you're wrong for many reasons: labor costs are not the only factor in determining where goods and services are produced; the dynamic you describe has feedback effects in the form of rising wages in the "cheap labor" country; it utterly ignores the near-certainty that the "expensive labor" country has parallel comparative advantages; productivity is a more important determinant in labor usage than raw labor costs; and geographic proximity to end markets is still important.

However, I think we've isolated why your analogy - while viscerally effective - is flawed. It is widely recognized that individuals, and even specific trades, can be losers under international trade regimes. So it is not surprising that an individual plumber may be hurt by such trade flows. But by failing to compare his losses to the appropriate community, you haven't really demonstrated whether the community is better or worse off. In order to claim that the community is worse off, you have to make a lot of assumptions in your analogy that are not readily apparent in the real world. Thus, the analogy loses its illustrative power.

Albaby