What should we tell the children about litigation, if anything?
Resist the temptation to involve your children in any aspect of the divorce. If the children are naturally curious or have heard statements about the litigation from your spouse or extended family, do not discount their feelings or questions. Calmly explain to them that these are adult issues that do not concern them.
Always take the high road. Your children are part you and part your spouse. Any criticism of your spouse reflects poorly on the self-esteem of your children. Find a balance between keeping the children out of the process and answering questions by explaining to them that everything will be alright, that both parents love them, and that the divorce will not affect that love and affection by both parents.
Children should certainly not be exposed to the details of court actions involving them. If your former spouse is willing, try going to a counselor or sitting down with a mutual and trusted friend to work out how to interact with your children in a positive and appropriate way. If that doesn't work, then consider court intervention. A judge can make specific orders for the protection of children, which may include orders to refrain from such discussion or, in some extreme cases, orders that limit or even supervise the access that the offending party may have to the child.