Welcome to the forum @Maeny. That is a difficult situation for you and you dad. I was accessing my parnter's account without POA, just for bills and food shopping, and it was Social Services who reported me to the police. The police detective recommended taking out POA or a third party mandate with the bank. If your nan won't grant POA I'm not sure what else to suggest.
The helpline is pretty good on legal and financial advice though if nobody else on the forum can help. https://www.alzheimers.org.uk/get-support/national-dementia-helpline
It depends on whether your mum has capacity or not.
My mum allowed me to have third party access on her accounts, but she would not grant POA. While she still had capacity this was legally OK, but once she lost capacity I had to apply for Court of Protection deputyship.
You can only apply for deputyship once capacity to grant POA has been lost, and its a lot of faff, but it was the only way
a warm welcome to DTP
I am surprised tha LA organised night time care, I guess they did it as your nan is self-funding
but if her capacity is in question and she has not granted LPAs then I think you are right to carefully consider how her fees are paid
strictly, someone should now apply to become her Deputy www.gov.uk/become-deputy/apply-deputy
unless your family honestly feel she has enough capacity to grasp that LPAs will give her Attorneys permission to help her and agrees at the time of signing (though if she's refused before, that may be an issue) www.gov.uk/power-of-attorney
if she can grant third party access, that may help ... and look into DWP appointeeship
Apply to become an appointee for someone claiming benefits - how to apply, stop being an appointee
The LA should have carried out a financial assessment after the assessment of her care needs, to check how close her finances are to the threasholds where the LA step in to contribute ... it's highly unlikely they will contribute to night care at home
personally, I think your dad needs to make clear to the LA that he has no legal authority to pay his mother's care fees and they must wait until either she herself agrees to payments being organised or for Deputyship ... but don't let them take on Deputyship as then a professional Deputy will be appointed
Not sure why the first post was deleted, but if someone has been having access to her account and unofficially settling bills, I don't see how they can suddenly say they can't pay the care bills because they don't have legal authority. It's either one or the other, and care bills need paying.