If you thought it was your job to prevent the other side from exercising custody, you haven't been paying attention to commonsense or the law. If the other parent is fit, or a court has found them to be fit, then it is your job as a parent to ensure the child benefits from the love and companionship of the other parent.
Take for instance the Pennsylvania statute:
§ 5303. Award of custody, pa
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Putting the child's needs first is the simplest and easiest way to convince the court that you are the more fit parent.... ...