Is a wife religiously obligated to travel with her husband, who wishes to travel to increase his wealth, given that she experiences hardship and aversion to travel, and does not feel safe with him?

If you did not stipulate in the marriage contract with your husband that he should not take you out of your country, then it is not permissible for you to refuse to travel and move to live with him in another country. You have no excuse in your attachment to your family, nor in his recklessness, as long as you are safe with him. The husband has the right to move with his wife from one country to another, even if she dislikes it, provided that the path and the destination are safe.