Is the wife's remoteness and insistence on working in another country a reason for the decrease in the husband's livelihood, despite his efforts, and his belief that God is the Provider, and that he heard that a man's keeping his wife at home brings blessing in sustenance?

It is not possible to determine with certainty the reason for a constricted livelihood, for Allah expands sustenance for whom He wills and restricts it according to His wisdom. Neither abundance nor scarcity of livelihood is an indicator of Allah's pleasure or displeasure. A wife's permissible work that does not affect her duties is not a cause for constricted livelihood. One should renew repentance and increase seeking forgiveness, for sins are the cause of afflictions, and piety is the cause of good. The general principle is that a woman remaining in her home is better, and the gathering of spouses is better than separation.