The only way to get a council house quickly is for your parents to evict them. If its affecting them that much they have to do it, even if they feel bad. They will have to move into temporary accomodation, its either that or nothing. I think your sister would rather take a bedsit then be on the street right?
It can sometimes be quite quick to get a council house when your in temporary, especially if its small and there are lots of problems, you get more points then. Its not so bad really, i dont understand why your sister wont live in a bed sit. sounds like she's a bit spoilt!
If your parents let them stay at theirs it will be a long wait. Tell them they need to do it now, it'll be the best thing for everyone.