After the green card, the whole family immigrated, including the spouse?

First of all, correct your concept: the act of getting a green card is immigration itself. Therefore, there is no so-called "family migration after green card".

Different countries have different immigration policies. Most countries handle immigration on a family basis, that is, including the main applicant of Ta and family members (spouse and minor children).

If you mean that someone got a green card first and then immigrated to Ta's family without a green card, then in this case, it should be a reunion of husband and wife and a reunion of minor children.

As for joining local nationality after obtaining a green card, it is handled on an individual basis. Once a person applies, it has nothing to do with family members.