Issues of Shalom Bayis (peace in the home) and any other deciding factor aside, does the husband have any "right" or "privilege" (from a halachic standpoint) to decide how his wife will cover her hair (tickle (kerchief), sheitel (wig), etc.)? Or for that matter can he decide on other issues of tznius (what type clothes his wife will wear, etc.)? I'm looking for sources in seforim, poskim, etc. if any exist (and not hashkafic answers based on experience, madrich chassanim (a bridegroom teacher), etc.).
Rabbi Moshe Feinstein clarifies his view in Igros Moshe EH4:32, sections 6 & 10, addressing Rabbi Elyakim [Getsel] Ellinson:
Nowadays a man can't divorce his wife because she refuses to cover her hair (at all.)
Generally a wife should adopt her husband's practices; however, what sort of hair covering she should use is her decision -- i.e. if she feels a sheitel is inadequate and would rather use a hat, he can't demand a sheitel; if she feels a sheitel is adequate, he can't prohibit it -- this is just totally private to her. However he may object if she wants to shave her head. Rabbi Ellinson saw these three stances as contradictory, to which Rabbi Feinstein politely replies he has no clue what Rabbi Ellinson means.
Well, a husband can divorce his wife and not pay her Ketuba money if she doesn't cover her hair "properly" (Shulchan Aruch Even HaEzer 115:1, 119:4). So if he is willing to threaten her with divorce then that would seem to give him a right (or at least an ability) to decide for her. That said, if the husband makes this threat it wouldn't surprise me if the wife decides she wants a divorce!
In general most poskim rule that the women has to adopt the customs of the husband. See for example Yabiah Omer vol. 1 OC 37 (and the many refrences there), Iggres Moshe OC 1:158, Halichos Shlomo Tefilla Chapter 1 footnote 7 and Techuman vol. 7 pg. 79 from Rabbi Chaim Dovid Halevi (past Cheif Rabbi of Tel Aviv).
R' Ovadia Yosef and R' Moshe Feinstein learn that the obligation is likened to a person who moves to a new place and does not plan to return who adopts the stringencys and leniencies of the new place. R' Shlomo Zalman Auerbach argues and maintains that the obligation stems from the fact that the wife is subservient (meshubad) to her husband.
Therefore if the husband's family custom is to dress in a certain manner of tznuius or cover women's hair in a certain way the wife is obligated to confine.