Is it considered minor shirk to force female relatives to wear the niqab only in their hometown to preserve the family's reputation, while allowing them not to wear it outside, knowing that minor shirk relates to acts of worship?

A woman is required to cover her face from non-mahram men. If a man permits his wife to uncover her face outside of his country, but obliges her to cover it in his country to avoid people's talk, there is no harm in that, and it is not considered shirk (polytheism) or hypocrisy. Rather, it is a praiseworthy sense of honor, a prevention of evil, and a protection for oneself and one's honor. A person may do something less preferred or non-obligatory for a predominant benefit, such as an Imam vocalizing the Basmala or abandoning Qunoot out of consideration for those who hold that view, or a traveler completing the prayer if the Imam is completing it, or standing up for an arrival to win hearts. This is not considered showing off (riyaa'), but rather an act of worship to Allah while considering the overall benefit. However, if a woman believes the niqab is obligatory but does not wear it in her country out of consideration for people, and uncovers her face outside of it even though she considers it a sin, then this is the flaw.