Should I tell my brother that my mother gave me the gold bracelet that he claims she was holding in trust, knowing that more than ten years have passed and I doubt his claim?

You are not obligated to give the bracelet to your brother unless he brings proof of his ownership of it.

If your mother owned the bracelet and gifted it to you, then it is recommended to return it to the estate so that each heir may take their share, unless the heirs forgive it. This would be a recommendation, not an obligation, because if the giver dies before reclaiming the gift, it becomes established for the one to whom it was given.