To ask for carers for my Mum when she doesn't want them?

YANBU to suggest carers.
YANBU to make it clear the extent you will/won't be able to assist her yourself.
YABU to force her to have carers.
YWBVU to threaten her in any way (a a pp suggested).

One way to suggest is to try, if she has money and can arrange herself she can agree to meet a few people to see if she can imagine them helping her. Go for individual rather than agency at this stage. Hopefully someone will be professional and she might be prepared to discuss the care she needs and is willing to accept

My mum refused carers.

You can't make someone have carers...

We had a similar situation with an elderly relative. Every time the carers came round he sent them away!

Social services will not "put her in a home" against her will either. In fact, they won't put her in a home at all because there is no indication that she requires this level of care. Telling otherwise to an elderly and vulnerable person as a way for them to agree to the "least bad option" is surely borderline abuse.

Tell her the alternative is that Social Services will put her in a home if they feel she can't look after herself!
Make sure she has both a Medical and a Financial LPA.

My dm also refused carers.

So we persuaded her to have a course of physio to improve her strength and then we organised a cleaner one morning a week, a gardener (2 mornings a week), a farm foods delivery, a weekly taxi ride to an old folks keep fit, a regular home chiropodist/ foot care and an emergency call button that she wore as a bracelet.
Plus a family visit most weekends.

It meant she always had a reason to get up and dressed. They all had my phone number if they thought something was wrong, and she didn't feel intruded on.

It took a bit of organisation but we managed to keep her in her own home until the last three weeks

If she doesn't want them that's her choice. She's not a child. Just make it clear to her you won't pick up the slack.

We did this as everybody was struggling however the family members in question cancelled them so back to square one.

Ask for ‘continuous healthcare’ its free and is for around 6 weeks i think

This will give her carers for a little while and she can then decide if she wants to keep them and how much help she needs

My parents were reluctant at first. Firstly they don’t want to acknowledge they’re getting old, plus it took a long time for them to get used to having them . Ie, telling them what to do.

Also it’s worth contacting g adult social services who can provide resources, equipment etc.

She can refuse them if she has capacity. However does your area have free carers for 6 weeks post discharge? And only after this time if you still need them you have to pay? There is also a difference between normal carers and enablement carers, maybe explain this to her? Ultimately even with the 'free' care package on discharge, if the carers find they are not needed they will pull out, even before the 6 weeks is up.
However she may be waiting ages for carers which might be why she is not keen, and the longer she spends in hospital the more de conditioned she will become, it's a bit of a vicious circle.
Has an OT assessed her certain function / care needs? What does she need help with atm? Has she got a falls alarm at her home? Does her area have a local falls prevention team she could be signposted to on discharge?

I was in a similar situation with my dad after he had an emergency op.
I focused on the two options, care home/rehab unit or carers so try that. Tell her that she will not be judged fit to return home so its either agree to visits at home, or don't go home.
Dad agreed to it on a trial basis, he didn't think he needed them but as I'd worked in care he eventually agreed to trust me. The 3 weeks without being able to have a pint helped! I reassured him that if they came and felt he didn't need them then it didn't have to continue. In the end, once he was home and they were visiting twice a day he realised it wasn't as awful as he had been imagining. He did 8-10 weeks of them visiting and then was recovered enough to stop the visits.
Reassure her that you can be there when they visit to start with, and that it doesn't mean you'll disappear either. Those were my dads fears.

Of course you can ask for them, but ultimately it's your mum's decision as long as she has the full capacity to decide for herself. If she's not able to go home without some help safely then the hospital staff can usually be quite persuasive and will make professional recommendations, but if your mum can show she understands the risks, can weigh up her decision etc then she can say no. Would she qualify for any help towards care costs at all? Some of it can be means tested, if it helps?
What will she do without the help? How would she manage? Is she expecting you to care for her? Ask her these questions and get her to really think about it, often it is a huge adjustment for older people to have to rely on others and accept they are no longer independent, and it's hard to accept so it could just take a little time?
Has she had OT and Physio and explored equipment etc that could help with independence too? X