Your whole story sounds incredibly challenging, and unlike many on your original thread, I have a ton of sympathy for the cycles of poverty that your family is trapped in. Many mustachians haven't lived in poverty and think that social services/government money are easy to come by and are available to everyone who should qualify. You are really trying to do the best in a bad situation/a hard society.
I used to live/work with specifically young mothers who need housing and social support. Most were women in recovery who had been incarcerated. Here are things that are effective when it comes to managing money that might be helpful when helping your sister/other family members:
1) They HAD to have their paychecks given over to the social worker they lived with (me) at each pay period. I did not go with them to get it but I knew when they got paid, and the expectation was that the check would be un-cashed and in my hand, by end of day on that day. This is the "don't work for them more than they are working for themselves."
2) This paycheck was then set aside to pay a flat fee for housing expenses (low-cost given that most of them were getting back on their feet with minimum wage jobs) and most of it was put into a savings account they had no access to that was saved up so that when they moved out, they had a financial cushion to use to pay a deposit with.
3) They were required to take a financial fitness class to learn about managing money- these are usually offered by nonprofits or community banks for free or very low cost. Look for one (maybe for all your family members!)
4) There was a "lock-out" period every day for about 4 hours in the middle of the day where they were required to go do SOMETHING - either go to work, go to the library, go to appointments. It didn't matter what, it was simply to ensure they were not just sitting in the house watching television (particularly because they had young children and those children do best when they are stimulated.)
5) They were forbidden from having their own car while they lived in the house. This was a requirement that occurred because while a car gives a great deal of access, unfortunately, it is a big financial burden (particularly for those with convictions that make their insurance rates sky high) and it also often gives addicts the access to social circles and places that cause them to relapse. The women in the house were required to take the bus or use bicycles with trailers (we provided them all with a class on biking safely with children.) Most women in the house found that biking was faster and better than the bus in our small town and said that the physical activity kept their heads clearer from addiction. This may not be an option for your sister given that it's South Jersey and I assume there's no decent transit - but perhaps the car that she has should in fact be your mother's for work, and your mother drives her to and from work and gets to use the car during the day for her cleaning business. This can help make sure your sister isn't using AND help your mom out with a car.
Find out the specifics of her testing- and +1 to what the poster said about recognizing that she may be substituting other addictions for her former one- even things you might not think of, like online flash games.