Different countries within the UK have different charging policies/ legislation for domiciliary care, so if your Mum is outside of England, the charges might not be as onerous as she thinks. It may also be possible to apply for disability benefits due to increased care needs, which would offset the costs. The hospital may have a discharge coordinator who could help fill out the forms, or Age UK or the CAB may be able to help- they know what to write to make care needs clear and increase the likelihood that a claim would be agreed.
A lot of people go the Direct Payments route, rather than using a care agency. This allows a person to have more control over their care, including who provides it and how. Staff are usually referred to as Personal Assistants rather than carers, which might help the idea of promoting independence rather than taking it away. The downside is having to find an alternative if the PA is sick or takes a holiday, as it is the employer's responsibility, not Social Services'.
It helps to get a Social Worker assessment, to ascertain their level of needs (hospital staff, as wonderful as they are, often don't see the 'big picture' of someone's life and circumstances) and can help signpost or refer to other services that could support once home.
As someone else posted above, let hospital staff know, and have it recorded in writing, that you are unable to offer reliable daily assistance, so they cannot include this option in discharge planning.
Good luck! 🤗