Then just leave. If they get home before you, they will see him sleeping. If they still blow up in your face and get all nasty, simply say in a calm tone "I've tried reasoning with the both of you. The dog is in no harm, and perfectly fine being left alone. I am no longer willing to put my life on hold because you *sister* cannot take responsibility for your own dog. Good day. *walk out, and or brace for impact*"
If she kicks you out, so be it. Bunk with a friend for a night or two until she comes to her senses. Or, start looking for a cheap studio flat.
Just my 2¢
I hope everything works out whatever happens!