1,809. If a Doubtfully-Divorced Woman Remarries

Hilchos Geirushin 10:2

Whenever the Rambam says that a get is unacceptable (pasul), the meaning is that it is only unacceptable under rabbinic law but the woman divorced by such a get is prohibited to kohanim according to the Torah. Such a woman should not remarry but if she does, she need not leave the second husband and their children are legitimate. Her first husband should give her a second, acceptable get. If this isn’t possible for some reason and her new husband is scrupulous in his observance, then it is praiseworthy for him to divorce her voluntarily so long as they have no children. If they do have children, he shouldn’t divorce her over the rabbinic disqualification of her get. This is because doing so would cast aspersions on their children’s reputations.

Hilchos Geirushin 10:3

When the Rambam says that a divorce is in doubt, the woman should not remarry. If she did so, she must leave the second husband and the legitimacy of their children is in doubt. If a man divorces his wife with an unacceptable get, or if the status of a divorce is in doubt, and he wants to remarry her, she is permitted to him. He does not have to remarry her with the seven marriage blessings or write her a new kesubah unless she has been divorced from him effectively.