It would be in the best interest of the dog -and your sister- to rehome the dog. Explain to your sister that giving him a new home would be good for him; she won't have to worry about caring for him or cleaning up his messes, either. I think when you bring it up, try and to tell her what she would rather hear instead of saying she's simply neglecting him.
I'll be wishing you and that handsome boy good luck.