Hi. Ok I would not bother with the he's tired speech. Divert, distract, ooh look a shiny thing, let's look over there.
It is a big ask of her sister to do an entire 3 days (2 sleeps?) so well done and thank you to her.
Moving forward, time to start thinking of what is best for Dad, do you think? Mum is at a stage where she can't be left, isn't she, it isn't safe. Dad is exhausted, and he needs to think of his own health and life.
Have a think about what Mum being safe and looked after looks like. It could be a home, where the activities are tailored, where nursing staff are on hand, where appropriate food is whipped up by Chef.
It could be at home, with more carers, maybe an overnight one if Mum is restless through the night. More hours with her two ladies? Food delivery/meals on wheels to take the pressure off Dad. A gardener, a cleaner, to take some of the drudge. Money obvs an issue here.
Consult community dementia nurse, get an up to date assessment, a carers assessment for Dad as well.
Gentle hand pat, very hard times lie ahead.