It's hard enough to study through the final years of school without the distraction of sharing your bedroom with someone who doesn't have any study commitments.
My thoughts would be to make it a temporary arrangement - give her x months to find a home of her own.
Maybe you should contact the Mum and give her a kick up the bum - wallowing is excusable and understandable but her daughter needs her now so it's time to step up and join the program. If she can straighten up and D can find a job they can share a flat - it would be the ideal solution (which is why it will probably never come to pass lol). I know you don't want to open up to her but I think you can call her without having to invite her into your home or commit to any kind of ongoing contact.