A Forced GET is Usually Invalid
by Rabbi Dovid E. Eidensohn
A husband who is not able to perform in marriage must give a GET according to the Talmud. But the Shulchan Aruch says that we don't beat him, nor can we do any serious kind of coercion. He may be told that he is wicked for not obeying the Talmud, but physical and fiscal pressure are forbidden.
Maharshal says that a husband who does great sins and is removed from Judaism cannot be forced to give a GET. However, the wife may leave his house and live with her family or alone.
If a husband is not one of the rare cases when a GET may be coerced from him, but he was forced, the GET is invalid. If the wife remarries with such an invalid GET, and has children, she is a sinner for living with a man while she is still married to her first husband, and her children are mamzerim. Nobody should ever call a child a mamzer or even say he is a mamzer until the matter has been checked out by a Torah authority who knows the laws of Gittin and has thoroughly investigated the case.
The Chasam Sofer says that when rabbis disagree if a husband should be coerced and the rabbis who permit coercion go ahead with it, the GET is invalid by Torah standards, meaning the children born from the woman in her new marriage are mamzerim diorayso. (Chasam Sofer Teshuvose I:28; and teshuva 116)
The gedolim in Israel have issued a pesak that no coercion should be done without their approval. Any Beth Din that coerces in ways contrary to the Shulchan Aruch EH 77:2 and 3 lose Chezkas Beis Din and we don't recognize their Gittin. Any woman divorced in such a Beth Din must have a new GET from an accepted Beth Din. The children born from such a Beth Din's GET must be investigated by an accepted Beth Din to see if their is some way to save them from mamzeruth.