You never know whether the cooperation/noncooperation will help or hurt your situation. When dh and I both went to try to annul our previous marriages we both faced people who would not cooperate or people we prayed would not cooperate.
First… nobody has seen my ex for years… not even his own mom! But yet in the end, his sister asked me if she could help by writing a statement to the tribunal for me… where my own family didn’t want to participate (thankfully my sister did return the paperwork)
Now with DH… he and his ex were not Catholic, but his ex is a nosy control freak and we have no idea to this day if she ever responded… but dear Lord his brother used the forms to tell the tribunal everything he thinks is wrong with the Catholic Church!
Both our cases went to different tribunals because of where he was confirmed and married Lutheran… and mine went to my own diocese… which is one of the toughest in the country.
Both of us were granted our decree of nullity for different reasons… but dh did have to go to counseling (about 4 sessions) before we could get married.
You really won’t know until you talk to a priest and start the process… don’t worry about who will or won’t participate.