Thats why there are halachos about picking a bais din to decide these things not a one sided bais din
you are missing the point. there are certain circumstances that are black and white and the main issue that is dealt with is does she have a zechus to be tovaih a get, these halachos are pretty clear,thats all that is imp, if she can then there is mitzva leshmoa if not - not, thats where mamzairus comes in. the technicalities of how the get will be done (costody ,money ect) is a small factor
the reason why they are causing mamzairim is because its very uncommon and unlikely to have a case where she has a zechus to be tovaih a get and he refuses to give. nothing to do with the divorce agreement