"Nobody else would do it properly"
This one is the standard again, pointed outwards. You've watched the agency carer do the breakfast and it wasn't how you'd do it. Your sister-in-law offered to take a Sunday and you said it was fine, because she doesn't know about the tablets. And underneath is a belief that your way is the way, and that anything less is a failure you'd be responsible for.
Some of it is true. You know things about your mother nobody else knows, which cup, which chair, what the sigh means. A stranger will get some of it wrong. But ask what "properly" is measuring. If it's safety, tablets on time and the cooker off, then that's a checklist, and checklists can be handed over. If it's the atmosphere, the exact way things are done, then you're measuring the carer against you, and no one will ever pass, which means you've built a test whose only purpose is to keep everyone else out.
Look at it from the chair. Your mother, most likely, does not want you to be the only person who can look after her. Being cared for by one exhausted person is not what most parents want for their children. Ask her, if she can be asked, whether she'd rather have the breakfast done slightly wrong by a cheerful woman on Tuesdays and have you on Sunday with nothing to prove, or have you do everything, tired, till you can't. Most parents, asked straight, choose the first. The ones who don't are chapter 16.
The link to guilt is this, and it's my reading. "Nobody else would do it properly" is the last defence of penance. It makes your exhaustion necessary. If you're the only one who can, then the weight is unavoidable and the guilt about wanting to put some of it down is justified. Take the belief away and the weight becomes a choice, which is frightening for a different reason, because a choice can be made differently. Chapter 20 is about making it on purpose.