Morning busy - how old is dd? Is she old enough to begin teaching her to tidy up and to get her involved in the declutter?
You could make the pile game I suggested earlier into a game - you pick up the item and discuss it, she puts it in the correct pile. I know it would take way longer but at least she wouldn't be wrecking another room while you were busy. You could still remove the bags of stuff afterwards when she was asleep or something.
Maybe if she had put the effort into tidying she would be less keen to wreck it again If she has to tidy the mess she makes she might reduce the mess after a while.
You could also do some sort of reward chart for her every time she tidies up or allows you to recycle something. I know sticker charts are done a lot but it might motivate her to clear the decks a bit. Make sure the final reward is a trip out rather than something new that will come into the house.
You could also get really ruthless about what you let in the house, at least until you have created some order and figured out some sort of storage system.
Would shelves work? If it was high up maybe she couldn't get at things without you asking her to get something down. That way you could teach her to put away before she gets something else out.
Praise, praise, praise any effort she makes to tidy, get rid of etc. It won't happen overnight but it will eventually.
Keep posting and we can keep trying to motivate and offer suggestions.