OP I was in this situation with mum - she passed away in March. She was very dependent on care at the end (vascular dementia) and it was becoming increasingly difficult so I understand where you’re coming from.
Can I ask how old your mum is and specifically what type of personal care you’re talking about ? Given that she has carers I would assume washing/bathing is taken care of daily and that toileting is attended to on each visit.
Mum had accidents and needed changing and washing in between carer visits which was unavoidable. I have to say I found it very difficult at first, because, as you say, she was a parent, and it’s definitely different. But you do get used to it and in the end I managed to do it without thinking because it’s a necessary part of care - you can’t leave someone in need until the next care visit.
This is the part of your post I’m having trouble with - But, obviously, these things are likely to come up in the future. What I was trying to convey was that I am here to do what's needed in the absence of the carers, and will do what is needed, but that not wanting to commit to being the default person to do my mother's personal care is my boundary. Surely my post explained it clearly enough?
To my mind if you have taken on the responsibility of looking after your mum in your own home, then you are the default carer. The care package she has is designed to take some of the pressure off you - it’s not there to absolve you of all responsibility. If I’m reading it right then the carers are asking you to take part in her care while they’re there. That’s not on and you need to set a firm boundary - with the care agency if it’s an ongoing problem - that you expect them to take full responsibility while they are there, regardless of your presence.
However - and before I get jumped on, this is just a question and absolutely not an accusation - at any point have they arrived and found your mum has been left in a mess for them to deal with ? Because equally that’s not on either and I would expect them to report that back to the agency as it suggests neglect. I only ask because you said in your OP Just been through it yet again with one of the carers this afternoon, and yet again I've been met with looks of incomprehension but you don’t specify what exactly it was that you went through with them. If they’re happy with the care you’re giving in between visits, what exactly is it that they’re expecting from you ?
From experience, as things deteriorate care plans have to be adjusted along with the number and types of visits, and at some point, if you really don’t want to be the ‘default’ carer, full time residential care will need to be considered. Obviously I don’t know your circumstances as regards funding but it does sound as though it will be necessary at some point because unfortunately the nature of this is that things will get worse, not better. I’m so sorry you’re having to deal with this, and kudos to you for opting to look after your mum at home - a very difficult choice.