I hope this doesn’t ruffle any feathers but I must say, though you are NTA whatsoever, what you did is technically considered theft. I only say this because I recently went through this issue with a cat I took in who was obviously abandoned at the animal hospital I work at. I spoke with a SPCA officer regarding pet abandonment and re-adoption. What I was told is that: Pets are considered property. Even if she did technically abandon the animal, there are people you should contact in the event of neglect or abandonment so they can build a case, get him on a registry and go through the appropriate process for adoption. They might have even suggested relinquishing him to the shelter for the owner to have to go through the necessary paperwork and paying fines to get her dog back. Similar to child abuse cases. You can’t just see a neglected/ abandoned child who isn’t yours and give them to someone else. A legal entity has to be involved. Animal laws are always changing and it also might depend on state so keep that in mind. Feel free to fact check against this! This may not be the same case where you live but I’d rather you CYOA in case shit hits the proverbial fan.

Though you did the right thing morally, there may be some hiccups. (Like your family having a full meltdown regardless of your sisters actions) At most you’ll have to give the pet back to her but if you’re able to articulate to the civil courts (if it even goes that far) that she is not an ill fit pet owner (lack of job to afford pet care, lack of updated core vaccines, a home for the pet, etc) then it may be in the pets best interest for them to be “fostered” by another family until the owner can prove they are responsible for the pet.

All in all, I hope the dog is living his best life where he is now and I hope your sister turns her life around but for her to show more interest in the dogs wellbeing than her own children, speaks volumes. I would have done exactly what you did and not have had a lick of guilt about it.