I want to tell my gf's sister one of her secrets
Are you kidding?
I'm extremely serious with this wish, maybe she deserves to know.
It is wrong to tell other peoples secrets especially if they can get hurt. People might not trust you anymore and stop confiding in you.
Why would it influence her trust towards me since she already knows the secret?
Your girlfriend thought you would keep her secret to yourself when she told it to you. If she wants her sister to know the secret, don't you think that should be up to her? If you tell her secret to her sister, you will lose her trust and harm your relationship.