Sounds like your sister prefers you as the caregiver, and she feels resentment or possibly that she does not measure up to your standards of care-giving. She feels lesser-than or incompetent around you, which would make sense with you having been the mother figure before. Stay as long as you need to, or as long as she will let you, but it is probably time for you to move out in order to save the peace and the relationship.
Your mother put you in a position of being co-dependent early in life (care-giver of everyone else, and putting your needs/wants, healthy child-desires away on a shelf somewhere). It is possible that you have harbored some of those co-dependent tendencies now, and that might be causing you some pain. If you are not familiar with co-dependency, you can research it on the web. It is not a negative to be co-dependent, you would just need to know and work around it. Just a suggestion, as in something to think about. I am not suggesting that you are co-dependent.
Just keep your chin up and one foot in front of the other. You're on the right path. One thing I have learned is that life will give you the same lesson over and over in different circumstances and situations until you learn the lesson to be learned. Best of luck to you.