Maybe you could just make up names for your sisters. I wouldn't use their real names.
It is your home. You invite whom you wish. You can't control what your mom and the others do. If they choose to go be with your alcoholic sister, that is their business.
So far as the girls go, it's good of you to help where you can but again, unless their mom's parental rights have been terminated, she has the final say in what they do. You might want to keep a journal of ways in which she has failed her parental responsibilities in case it ever becomes necessary to get child protective services involved.
Yes, it is a three-ring circus you have going on there right now. Do your best to take care of your own responsibilities and let others handle their own decisions.
Have you been able to make it to Al-Anon yet?