If the other parent refuses to go through private mediation, then demanding it is not going to accomplish very much. Some states require mediation with a court appointed “mediator” (or counselor) prior to the court hearing.
In such cases, the recommendation of the court facilitator is usually adopted. In the courtroom itself, one could point out the difficulties in co-parenting, and ask for co-parenting counseling to be ordered.
Then the other parent is compelled to attend. A refusal to do so would certainly make the other parent look like a lousy co-parent.
However, there is a trade-off in all this for the dad: co-parenting difficulties usually sways custody in favor of the mother… so weigh the balance in your personal situation carefully. PS- coank, since you seem to be in a reading phase, check out our NEWS/Negotiation section (recently added).
Personally I recommend the works of Ury at Harvard Law. Good luck.