Ask someone at the morgue what paper you need and how you can get it. There will be a court record.
Did your mother adopt her grandson or did she become legal guardian? Adoption papers would be on file in the States Bureau of Vital Statistics. Some states allow you to get copies over the Internet. Others require that you get them thru the mail or in person.
When "they" turned over custody to you,how did they do it? Did you adopt or become legal guardian or thru a different legal process? I'm unfamiliar with the process resulting from death. This may have happened because of a will and I don't know how that's handled.
If you don't want to go back there, I suggest that you can obtain copies of legal documents and then send them along with a notarized document giving your other sister the right to obtain the body for you.
The best place to start with this is with the morgue. Ask what they need to release the body. If you don't have those papers when you arrive you'll still have to wait to get them.
I am so sorry that you're having to deal with this. I send my condolences.
Later: Ina G.'s suggestion helped me think of another idea. If you have a report card from his school years that may have you listed as parent/legal guardian and might work.