question : Would you believe your child if they told you they’ve been sexually molested?

No, not unless they also provide some form of proof to confirm the claim. If I don’t have a reason to think the kid is lying or that the claim is otherwise untrue, however, I would take any appropriate legal action on the kid’s behalf. As the parent or guardian; a hypothetical fact implied by the word “your”; I’d feel morally obligated to do so. I’d just make sure that, when I go to file the police report or whatever, I present the allegation as the kid’s and not my own.