We got her admitted, so now on to the next step. Any other suggestions?

Agreed.....I am not able to provide care for her. I will visit her for social visits when I can, wherever she is located.
It would be unsafe to discharge her home with services as she will not accept them.
She does not know what to do in case of an emergency - smell of smoke, fire alarm going off, water pipe breaks and floods her living area.

Let the state find a location and a guardian for her. (manages money and health decisions).
You can continue to be a supportive family member. Same for other cousin.
Hospice support might be a good idea, wherever she ends up living when she leaves the acute care hospital.

Excellent. Remind the Social Services at least daily that it is crucial you speak to them. Do not argue with them. Do not let them say "She can come home and we can help and we can make this work." That is a lie. They can't and they won't. Insist on placement. Don't accept POA if she is competent, nor guardianship if not. Let the state do it. If you DO it know it is a hard job and you will be responsible for everything, and its management and accounting for every cent in and out of her accounts.
Start backing away now. Call daily to let them know she cannot safely return home and has no one to manage her life for her and needs social service for placement. If you are constantly there they will eyeball you as the logical choice for a life of misery ongoing dealing with Aunt.

Maine, good luck.

The Next Step is to stand strong about "safe discharge".

Good luck!

shes Actually admitted. That’s good.

is this an aunt? She should care but probably doesn’t that you stepped up.