Avi: I mentioned violence and abondonment are valid halachic causes for mandatory divorce. Note, though, that S”A rules that the halacha is that the beis din needs to give him a second chance – under warning – that if he doesn’t correct his behavior they’ll require him to divorce. Also note that the S”A rules that if he denies the allegations of violence, eyewitness testimony to that effect is required for beis din to have the ability to order a divorce. The S”A states that the beis din can put an agent in their home to bear witness if her allegations against him are true. Allegations regarding verbal/emotional abuse, though, are not specified in the Gemora that Chazal give as a valid cause for mandatory divorce. And the S”A rules that a beis din can only tell him he is obligated to divorce in circumstances that Chazal specifically list as a valid halachic cause for an obligatory divorce.
As far as the New York (or anywhere in the U.S. for that matter), no court can jail someone for not giving a Get. As noted, only the plaintiff filing the case is required to submit that form. That form needs to be submitted together with the initial divorce petition. And even if the husband is the plaintiff filing the case and he fails to submit that form, the court will not accept the case until it is filed, and deem his submission defective (no differently than if he failed to file any other required paperwork when filing a case) and the court won’t act on his filing.
And Rav Elyashev and many other poskim have issued a psak that if a wife invokes New York’s (second) Get Law in order to financially penalize her husband in marital asset distribution by the secular court when he didn’t issue a Get, then the resulting Get is invalid (Get Me’usa).