My turn. I know nothing about this case, so any comments are only about the subject matter in general.
Batei Din have both parties sign a Shtar Berurin, essentially an arbitration contract that obligates them to accept the decision. If a beis din is corrupt, all sorts of shenanigans can occur, and sometimes do. However, the document ends up in court, not always an arkaos problem because divorces and custody matters need the official psak from court. Many batei din have this shtar written and signed in Hebrew and in English. This shtar/document is now a legal contract, and one needs to follow it to the letter of the law, regardless of whether it is fair or not. Batei din are perceived to be unfair to women, but that is usually not true. Either side can manipulate, fabricate, withhold evidence, and this gets reflected in the proceedings in beis din.
If a custodial parent fails to raise children according to the agreed religious lifestyle, then there is a violation that will be addressed by the court as breaking the arbitration agreement.
There are cases where women claim to continue living a frum lifestyle, just not chassidish, but are really living as goyim (except to dress up for the court). This needs to be documented, and challenged as a breach of the arbitration agreement.
No one is “forced” to sign anything. If they do so, without reviewing it, they might have signed away a lot, and there may not be any recourse for them.
Lastly, using a get as “ransom” is intolerable, no matter who does it. However, it is foolish to conclude the marriage with the get when the other matters of the breakup (settling issues of custody, division of property, financial agreements, etc) have not been completed first. Most batei din follow this path, and it is reasonable. If the two sides do not agree, no one is “withholding” the get.