To 646:
The Beis Din has the option of allowing the court to rule on custody. If so, there will be permission granted, and this should always be in writing. However, it is unwise to have the get given when issues such as custody are still not resolved. Beis Din does NOT use withholding of the get as a threat. They can note, usually with full justification that since matters are still not resolved, the get would not be a true krisus, and should not be done yet. Beis din does not threaten.
It is common for people to avoid going to the beis din that is part of their immediate community for obvious social reasons. They are free to look for other batei din, and our community has many options. No one is forced to go a specific beis din. There is NO abuse of power or force.