I dont think bringing up the past in custody court will be useful. Unless what the other parent has done in the past has shown to be harmful to the children and that behavior could be deemed to continue, then it is worth bringing up. But your best bet is to focus on the future plans for the children.
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The Parent's Observable Behavior in Court A parent's behavior in court will play a significant factor in determining custody. Being argumentative or expressing hostility towards the other parent will be noticed by the judge. Likewise, being reasonable, cooperative and respectful towards the court will help. In court behavior alone will not determine custody, but it can certainly help tip the odds one way or the other, and should not be ignored.