Is marrying a third wife to accompany the husband on his travels, while leaving the first two wives in their homeland, considered a sin or an injustice to them?

There is no harm in marrying a third wife, provided there is justice. However, the wife is not allowed to refuse her husband's travel with her, and the husband may draw lots among them to determine who will travel with him.

It is not permissible to marry a third wife for her to reside with the husband without the consent of the other two wives, because it contradicts the obligatory justice, unless they agree to waive their right to spend nights with him while he is abroad. Otherwise, he must reside with them just as he resides with the third wife.