One of the important changes in divorce law resulted from the decree of Rabbeinu Gershom that a woman can not be divorced against her will - despite the fact that she can be divorced against her will according to Torah law. Therefore in modern times if a woman refuses to accept a get - her husband can not remarry unless he gets a Heter Meah Rabbonim which indicates that decree of Rabbeinu Gershom does not apply in his case. The HMR isn't a divorce but an allowance for bigamy. There are also questions as to whether this decree was made for a limited time- and therefore is not applicable anymore and also that it was not universally accepted.
As we have been discussing the question of what happens if the halacha is violated and the husband is forced to give a get - is this get totally invalid or only on the rabbinic level - there is a similar question regarding forcing a get on a woman. Is the Get good bedieved or is the get invalidated? This is discussed at length in the Sdei Chemed.
The significance of this question is obvious. If a husband is fed up with his wife's extortion or use of secular courts - what would happen if he simply forced her to accept a get? Or alternatively if the husband uses the threat of a forced get to extort better terms from his wife - is it a genuine threat? What if he remarried after a forced get without a Heter Meah Rabbonim? Even more more problematic - what if she remarried after receiving a forced get? Would her children be mamzerim? Would she be forced to leave that marriage?
Shulchan Aruch (E.H. 119:6): A woman can be divorced against her will. REMA: Even if he doesn't have sufficient funds to pay her kesuba or dowry - that does not prevent the divorce from working. He should divorce her and then she should take him to beis din to collect what is owed her. All of this is according to the law of the Torah. However Rabbeinu Gershom decreed that a man can not divorce his wife unless she agrees and if he does he transgresses the religious law...So even if he want to give her her kesuba - he can not divorce her today against her will. If he transgresses this prohibition of Rabbeinu Gershom in modern times and then remarries he can no longer be called a sinner
Shulchan Aruch (E.H. 119:6): A woman can be divorced against her will. REMA: Even if he doesn't have sufficient funds to pay her kesuba or dowry - that does not prevent the divorce from working. He should divorce her and then she should take him to beis din to collect what is owed her. All of this is according to the law of the Torah. However Rabbeinu Gershom decreed that a man can not divorce his wife unless she agrees and if he does he transgresses the religious law...So even if he want to give her her kesuba - he can not divorce her today against her will. If he transgresses this prohibition of Rabbeinu Gershom in modern times and then remarries he can no longer be called a sinner