In the Torah a father is given the right to marry off his daughter before she's an adult. Does this work even for nissuin (the second stage of marriage) or only arusin?
המארס בתו קטנה, ותבעה הבעל לנישואין - בין היא בין אביה יכולין לעכב, שלא תינשא עד שתגדיל ותיעשה נערה. ואם רצו וכנסה, כונס; ואין ראוי לעשות כן.
One who effects erusin on behalf of his minor daughter, and the husband then wishes to perform nissuin, either the father or the daughter can prevent this from taking place, so that nissuin will not occur until she grows up and becomes a na'arah. But if they wish for him to perform nissuin he may; however it is not correct to do so.
Thus, the father has a veto over his minor daughter's nissuin, but he also cannot allow the nissuin to take effect against her will (unlike erusin).
In any event, Rambam rules that it's not proper to effect nissuin with a minor, even if all parties consent.