I’ve been trying to put out a few feelers locally to find her some more families but no luck so far.
Well, it's time for her to start figuring out an income out for herself. Or do without fancy haircare products.
when your self esteem is already low, the last thing you need is for your hair to look rubbish.
Don't project onto her a connection between low self esteem and haircare products. As long as she's still washing her hair regularly she is doing OK.
dd is still continuing to argue that if we want her to do things, it has to be requested from me not Dh.
That's a power game so don't play along. Keep repeating "you have two parents, either of us can ask you to do things" and "you have two parents, you must listen to both of us" and "you have two parents, if Dad tells you to do it then you need to do it". It wont work straight away. She is persistent and she'll keep trying. You and DH need to keep going and be more (gently) persistent than she is.
And if she does what Dad asks, she gets the allowance or whatever. If she doesn't do it, no allowance.
One of my friends had some pocket-money chores and the kids got a bonus if they did a chore straight away no arguments. Her kids were 8 years old but your DD is still operating at around that maturity so it might work.