Can a husband stop his wife from covering her head? What if the husband is so opposed to the idea of his wife covering her head that it can lead to a divorce? Then what is one supposed to do?

A husband has no authority to stop his wife from covering her head. He cannot overrule the directives of the Almighty.

As far as the second part of the question is concerned, a woman can seek divorce from her husband on these grounds if she can bear the consequences of such a divorce. Allah will definitely reward her for this. However, she must be very realistic in this regard. Facing the consequences of divorce is not easy at all in this society. If she thinks that this would be too much for her, then, of course, she has a genuine excuse to continue with her husband. She must know that Allah never requires of a person something which is not in his or her control and always entertains legitimate pleas.