Which term implies that a married couple is living independently and away from both sets of in-laws?

The term is NEOLOCAL

The term "neolocal" is used when a couple, usually newly married, resides away from the relatives of the wife and the husband's. In this form of post-marital residence, which is most common in industrialized countries (Australia, The United States, Canada, etc.) couples tend to form a nuclear family.

Neolocality would be the correct answer

definitely a for sure. ill see and update if i get the answer