Hello, yes POAs (both health/welfare and financial, for both her and your Dad) are a key step and some financial planning/advice are a good idea. You can start to research local domiciliary care agencies and perhaps even have some conversations about cost, I would highly recommend using an agency rather than directly employing as that way the recruitment/vetting/training/support for the carer is taken off your hands and holiday/sickness/other absence cover is provided and if there are any issues with the carer you can take them up through the agency rather than trying to manage yourself from afar, probably this will be more expensive than just employing one person directly but I think safer/more reliable.
It's great that you are able to have this open conversation with your parents, what I would say though is that you might need a bit more of a conversation about when/how the plan for full time care is enacted, you might think it's obvious but actually a lot of older people manage fine with relatively minimal input for a long time, even their whole lives, some do of course end up needing residential/full time care but they rarely go between the two states overnight or in a very sudden/clear way, there's often more of a gradual decline where the person themselves doesn't perceive themselves as struggling/needing as much help as they do (which can be part of emerging dementia but can also be simple unwillingness/inability to accept their increasing age or frailty).
It's fine that your Mum is saying she doesn't want to go into a home and would rather have live-in care, but I think it's more likely they'll end up needing a stepped up/tiered approach over the years, so Tier/Step 1 might be having some domestic assistance, gardeners, cleaners, maybe budgeting a bit more for food so as to have more easy/convenient options, Tier/Step 2 might be visiting carers to help with dressing/medication, meals service, laundry service etc, Tier/Step 3 is a live in carer but who only works normal/daytime hours, sleeps at night and can have weekends/holidays off with family covering other times, Tier/Step 4 is genuine 24/7 cover for which you'll need a team of carers (or consider residential at this point, I know that's not your mum's wish but at that stage where illness is so severe a home can genuinely be the kindest option). I'm not saying you need to get deep down into the detail as obviously you won't know her/their needs yet and of course many people do manage their whole lives without progressing all the way to stage 4 or even past stage 1, what I'm getting at is it would be useful to start preparing and thinking about how will she and you know when their needs are changing and when will extra support be put in place. Do bear in mind your local authority will be able to help to a certain extent with care/social needs, yes it's means tested and your parents will likely have to contribute given their financial situation but still worth exploring using when the need arises as they've done the hard work of sourcing an agency (not always easy) - most local authorities won't offer live-in care but 3-4 visits a day for the more able is possible and you can then supplement with your own private additional care or other support e.g. cleaning. Age Concern provide lots of care services (again you do have to pay) so worth looking at their site...