Can the baby sleep in your room, and the 6 yo in the other on the same floor?
It's a big change for her given what she is used to, and it's sounds like the dependence is encouraged and enabled by your partner, who I'm sure loves his dd and only wants what's best..
He needs to be the one to encourage her to sleep on the other floor, and it doesn't sound like he is prepared to

I'm not sure whether there's anything you can do I really feel it has income from him.

What does her school teacher or her mum think of her staying up so late? What are her sleeping arrangements at her mums house?
Are there any underlying gears or anxiety that either your partner or his dd may have?