This dynamic is bound to incite strong emotions. Then the dumper feels provoked and fights back with accusations and recrimination. It is no surprise that divorcing parents may experience trouble collaborating after this. If a divorcing couple is going to cooperate at all in parenting, some degree of trust must be re-established. Even though you may not feel it possible to trust this person completely, that doesn't mean you can't define very specific areas that you can trust.
Some people have trouble even imagining a form of trust.
You've got to be kidding. Sometimes divorced spouses will balk at this, saying they can't think of anything they can trust. But if they share parenting at all, chances are they are already experimenting to see what they can count on. They see they are already willing to believe in a few things, so now they can identify others. Just as important is not to trust your ex-spouse in areas where you truly do not have confidence.