This poor child has been through so much, I cannot fathom the pain and the nightmares.
I'm sure you have worked with the professionals and you know that fear of rejection is so huge in traumatized and "shuffled-around" kids, and this will be with her forever. You have made great strides but there will away she something there. Structure is really important for insecure kids so they know exactly what to expect. Yes, they do test you sometimes to see how naughty or defiant they can be, to see if you will get tired enough to send them away.
I'm sure that someone else told you that, poor eating habits aside (which can come from neglect), eating disorders are very often a form of control There is so little that kids can control in their lives anyway, but a child who ha been a human ping pong ball and tossed around a lot is going to work even harder to find something, anything, that is within her own power. Eating, sleeping and bathroom habits are really the main areas they can control, from toddler age on. If the professionals have told you not to ever let her have certain foods, that's one thing. But kids who want a little snack food now and then are totally normal - so decide whether it's okay to let them cheat a little unless there's a compelling medical and psychological reason not to.
Now, all kids have issues with chores. So part of what she is doing is completely normal. When they start to get a little hormonal from 11 on, it can get worse. What can you do to make it easier though? How about a towel rack on the back of the bedroom door so that taking it back to the bathroom is not as big a chore? How about a hamper in the closet so that clothes don't have to come down the hall to the main hamper? How about a written checklist on their bulletin board or on the back of the door? Can you put a few hooks in the shower so that the washcloths have a place to hang and drain, right there under their noses? I'm not sure why the floor is wet - do you mean the bedroom floor because they are going in there still dripping? Or do you mean the bathroom floor? Are they not using a bathmat?
I love the idea of a ring or any other token that reminds them that they are chosen kids, chosen by you, and permanent. You could also wear a locket with their pictures inside - seeing the jewelry on you at all times might be reassuring!
But structure is also reassuring - letting them know that you have expectations and that's because you love them and know they are capable. They are members of your family, and that's what families do. I wouldn't emphasize right now that they will need these skills when they go out on their own after high school. Right now they don't need to think at all about being anywhere else besides with you.
I'd talk to the doctor who told her she has PTSD and discuss the issue of an "excuse" - has she said it's the reason she doesn't do stuff? Or is that your analysis? Are you all in family counseling? That can be very helpful for you in learning how to deal with them, and in understanding what they do and say - you know, what is an indicator of a deeper problem, and what is typical kid stuff. I think it will help as you head into adolescence when kids are struggling to find themselves and figure out how they fit in the world.
Finally, with all kids, it's about choosing your battles. For example, if the wet floor is the biggest problem, maybe let the washcloths in the tub slide. You could ASK them which is better, a bathmat in the bathroom and they do their drying off and dressing there, or a towel rack in the bedroom. Control is important but give them choices that you are happy with no matter which was they go.