What is the legal (Sharia) opinion regarding a wife's stance on her husband traveling to another country for work, given her awareness of her parents' strong objection to it, and the husband's desire for a better future, despite the availability of a current source of income?

If you did not stipulate in the marriage contract with your husband that you would not leave your country, then it is obligatory for you to obey him in moving to the country he desires, as long as the travel is safe. Obedience to the husband in this case takes precedence over obedience to parents, but you must still honor your parents and be kind to them. It is important to be cautious about residing in the lands of the disbelievers due to the dangers it poses to religion and morals.