You sound like a fantastically caring daughter, your whole family sound so wonderfully caring looking after your Nan for so long. I’m sure you’re an amazing support to your Mum and hat she really appreciates it.

I work in social care, albeit not elderly but my advice is that it’s never too early to start getting the professionals involved. Your Mum is coping now but for the current situation to continue the family needs help. You family carers are saving the government so so much money, it’s hugely under-appreciated.
I’d be encouraging your mum to call the social work department for an assessment of your Nan’s needs and to be quite firm with them that the family needs help- carers/respite/whatever you all feel would be best.

One thing I would say to your Mum is that there will be all sorts of things that only she can do, mainly around making decisions and "managing" all the bits of the jigsaw that go towards keeping your nan safe and happy. And of course your Mum having happy mother-daughter time with your nan.

So get outside help - eg social services - for absolutely anything else you can, to preserve your mothers energies for the decision making/managing role.

It's too easy to start taking on extra little bits, none of which seem much in themselves, but which lead you to become overwhelmed. So if you can persuade your mother of all this, you'll be doing them both a service. Remember, no-one can care for anyone else unless they're in a healthy state themselves. So your Mum's first priority has to be her own health, because without that, she can't support your nan, or, indeed, you.

You sound lovely OP.
But I do agree with @DowntonCrabby, getting the professionals in as early as possible you just don't know how quickly she may deteriorate. My mum went from living on her own, to living in a home within 7 weeks. We were very very lucky we managed to find a bed for her so quickly. But I don't know what we would have done if we hadn't.
Ask social services for a care needs assessment for a vulnerable adult. Even if at this early stage, they determine no help is required (although if your mum is having to take time off work then it sounds like some help is required) you're in the system, it'll be easier to call and say nans condition has deteriorated, than have to start the whole of the process.
Think of worst case scenario, what if something happened to your mum, ie she broke her leg or arm, she probably wouldn't be able to care for your nan as she does now.
Hope you get sorted

Can your parents afford a cleaner? It would be one less thing for them to do when they get home after a long day.

I realise this post is almost a month old now but I would also advise your mum to see if she can get onto the Admirals Nurse organisation (you can find them through google etc). They are there to support the families of people with dementia. They can help you find your way through the system.

When my mum was diagnosed a few years ago, our Admirals Nurse helped me apply for a blue badge. She explained that I should try for one because taking mum out would be tiring for her. For example, having to concentrate in the supermarket when you not only don't recall where apples would normally be but you've forgotten what an apple is momentarily may make her very tired. Trying to drag a tired person with dementia across a car park is like persuading a very big toddler to come with you when they don't want to. Leaving them whilst you get the car isn't an option in the latter stages because of the potential to wander.

And, if your Nan has a diagnosis of dementia she is entitled to Attendance Allowance. It's not means tested and can be used on anything that makes life easier for her. So we used mum's initially on a cleaner each week and a mobile hairdresser as she couldn't go out easily on her own and we were working. Later she used it to help towards a Day Centre cost then extra carers coming in. The Department for Works and Pensions can help with that.