Moreover, he transgressed the law of our fathers and married Glaphyra, the daughter of Archelaus, who had been the wife of his brother Alexander, which Alexander had three children by her, while it was a thing detestable among the Jews to marry the brother's wife.
You may, as I was, be thinking, "But the Torah commands levirate marriage!" In fact, the Torah commands levirate marriage when the deceased has left no children. When he has, there is no mitzva, so Josephus is not contradicting the Torah to describe it as "detestable".
Archelaus, at the beginning of his reign, was welcomed as a great relief from his murderous father; however, after ten years, "his brethren, and the principal men of Judea and Samaria, not being able to bear his barbarous and tyrannical usage of them, accused him before Caesar." XVII.13.344:
Caesar, upon hearing what certain accusers of his had to say, and what reply he could make, both banished him, and appointed Vienna, a city of Gaul, to be the place of his habitation, and took his money away from him.
One doesn't think of kings of the Jews as being exiled to Vienna, but it did happen. (Or at least, to Vienne, in western France rather than the capital of Austria, Vienna being the name it had under the Romans.)
XVII.13.350 reveals an attitude towards remarriage suggestive (and possibly not surprisingly, given the time) of Christianity, rather than Judaism:
Glaphyra [...] was the daughter of king Archelaus, who, as I said before, was married, while she was a virgin, to Alexander, the son of Herod, and brother of Archelaus; but since it fell out so that Alexander was slain by his father, she was married to Juba, the king of Lybia; and when he was dead, and she lived in widowhood in Cappadocia with her father, Archelaus divorced his former wife Mariamne, and married her, so great was his affection for this Glaphyra; who, during her marriage to him, saw the following dream: She thought she saw Alexander standing by her, at which she rejoiced, and embraced him with great affection; but that he complained to her, and said, O Glaphyra! thou provest that saying to be true, which assures us that women are not to be trusted. Didst not thou pledge thy faith to me? and wast not thou married to me when thou wast a virgin? and had we not children between us? Yet hast thou forgotten the affection I bare to thee, out of a desire of a second husband. Nor hast thou been satisfied with that injury thou didst me, but thou hast been so bold as to procure thee a third husband to lie by thee, and in an indecent and imprudent manner hast entered into my house, and hast been married to Archelaus, thy husband and my brother. However, I will not forget thy former kind affection for me, but will set thee free from every such reproachful action, and cause thee to be mine again, as thou once wast. When she had related this to her female companions, in a few days' time she departed this life.
In modern Judaism the period of mourning, which is eleven months for other close relations, is reduced to just one month for spouses, to allow speedy remarrying, for, as it says in Genesis 2, "It is not good for man to be alone."