You are right to be concerned. Not only are your children in danger, but if they are regarded as "residents" of your ex's household, they are barred from making a claim under the homeowners or renters insurance policy. To solve this problem, you need to talk to your divorce lawyer. You and that attorney might decide that a custody order modification would be beneficial. To assist in proving the dog is vicious, the divorce lawyer could seek input from an animal behaviorist or attorney who has experience in dog bite cases.