If a child is thought to be abused by a parent seeking his return under the Hague Convention, will the court refuse to send him back?

Not necessarily. Even where the court has no doubt about the child being abused, the removing parent will have to bring clear and convincing evidence of abuse, and that returning the child would expose him to a 'grave risk' of physical or psychological harm, or put him in an 'intolerable position'. Even then the court has discretion about returning the child or not. Proving 'grave risk' defences is very difficult, and it should be remembered that the child is not being returned to the alleged abuser's custody – but to the home country where it is presumed that appropriate action can be taken to protect the child.
Convention In Action