Frank & Disillusioned: I’m simply speaking from Halacha. According to Jewish law if a man does not wish to divorce, he is not required to. And if he’s forced to give a Get under those circumstances, the Get that’s given is deemed by Halacha to be a Get Me’usa, an invalid Get. Even if he was incorrectly forced to give it by a beis din. (Let alone if he’s forced to give it by thugs threatening him.) All this is written in the Shulchan Aruch. So he’s still married to his wife according to Halacha even though he gave her a Get (Me’usa.) Therefore if she remarries she’s committing adultery and any future children are mamzerim since she’s still halachicly married to her first husband.
Of course there are a very limited number of circumstances that Halacha permits a Beis Din (and only a B”D) forcing a husband to give a Get against his will. But the only such circumstances that it’s permitted according to Halacha are the small number of precisely described circumstances that Chazal permit it (i.e. he has a physical deformity, or he habitually hits her and has been warned to stop and there’s proof he continues). Any other circumstance where he’s forced to give it, that aren’t one of the circumstances that Chazal described, the result is a Get Me’usa, per the Shulchan Aruch.
Similarly, Rabbeinu Gershom gave Ashkenazic wives the right to choose to refuse to accept a divorce that her husband wants to give her, if she wishes to remain married to him despite his desire to divorce her.