hello
@MetalKnee16
a warm welcome to TP
it's quite a theme, I'm afraid, that we as children feel that our parent/s are needing some support and care, but the parent themselves doesn't agree and doesn't want to have anything change, as they are 'doing just fine on their own'
you're doing pretty well if your dad is considering sheltered accommodation, as often there's a complete refusal to consider any move - so might it be worth going ahead with organising such a move for them, so that they are near you and it's easier for you to support and intervene - it would at least put your mind more at rest - and give you a chance to see how they really are day to day
then, when they are both close by, it will also be more straight forward to get some support in place for them - contact their Local Authority Adult Services for an assessment of the care needs of each of them; they have a right to this
any chance of suggesting a cleaner who just happens to be happy to cook or warm up pre-prepared meals for them too?
you imply that neither a diagnosis - though that's secondary if they have capacity to make their own decisions and can agree to a move and sign any documents needed (while you actually do all the background work for them, so they don't have to be anxious about it)
you can write to their GP and explain any changes in your mum that you have noticed and outline your concerns - some then invite the person to a ' routine well woman' check up for 'everyone their age' and include a memory test - or has your mum had her flu jab?
do you have LPAs in place for them as these will give you legal authority to support them in managing their affairs and to take over if that becomes necessary
of course finance can be an issue in any move, so I appreciate this may not be a simple solution (are there ever any?) - and it can be worth moving into a care home sooner rather than later - it's not necessarily the case that your dad wouldn't be able to go out for a walk; that's something to bring up with each home you consider
there's lots of help and useful suggestions on offer here, so do keep posting - maybe start a thread of your own to get more response
maybe here
https://forum.alzheimers.org.uk/forums/i-care-for-a-person-with-dementia.70/