How do I deal with a family member who has the “YOLO” (you only live once) mindset towards our disabled father?

I hate to say it but....I am sort of in your sisters camp here.
I know that leaves you to deal with regulating blood sugar later on and other potential problems but....
You know your dad is not going to "get better"
You do know your dad will probably have stroke that (hate to be blunt here but..) that will take his life. (better to take his life then leave him totally incapacitated)
You know the dementia will get worse.
So let him have a slice of cake. Maybe talk your sister into ordering cake that has a bit less frosting, or order a slice of apple pie, at least he will get a partial serving of fruit ;)
Now if she were taking him sky diving or rock climbing my answer might be a bid different.
And I know you need a break but maybe once in a while meet them and have a piece of cake yourself. Let your sister still be the caregiver for the day you just be a sister and a daughter. We all need to let go once in a while.
Again this brings to mind the Tim McGraw song...Live Like You Were Dying....

You might want to educate your sister and yourself more on controlling blood sugars by when and what type of sweets are consumed. Sweets on an empty stomach impacts blood sugar much more than the same sweet eaten after a meal that included proteins and healthy fats. A little peanut butter, low carb ice cream, or whipped cream reduces the spike of many sweets. I was shocked to discover that adding some ice cream to my pecan pie reduced the blood sugar spike by more than 50 points. Even a moderate increase in activity allows someone to eat some extra sweets without a big blood sugar spike. Is you father willing to take a walk after lunch?

My mother has a sweet tooth; she isn't diabetic but she has multiple siblings and a child that are (with a few others pre-diabetic) so I try to moderate the sweets in our diet so she doesn't develop geriatric diabetes. A low carb "smoothie" made from sugar free angel cake, carb smart ice cream and frozen strawberries has a rich taste with the same carb load as a roll. I make pound cakes with splenda baking mix that have a sweet taste and lower carb load because they don't need any/much icing. Banana bread with a little cream cheese or fresh fruit (apples, tangerines, nectarines) taste sweet with a much lower carb load than candy. A chocolate chip pan cookie served with a small scoop of ice cream raises blood sugar less than just a plain cookie (although it will remain elevated at the lower level longer). I try to feed her sweet tooth with regular doses of these "relatively" low sugar options so she doesn't feel deprived. On Sunday we have a meal with 2 carb loaded items (usually pasta/potatoes and corn/peas/carrots plus bread and a rich desert. Her A1C is around 5.4 and mine is 4.9.

Obviously you want to control blood sugar spikes enough so that your father isn't impacted with bad side effects. Mild spikes aren't likely to have major consequences but can allow your father to live a little. If you can find a balance with the lower sugar options so that your father isn't complaining so much you may find he cooperates more on the weekends with the major sweets too.

Good luck. Care giving has a lot of "components" and stresses the non-caregiver may never understand. Your sister probably doesn't understand the extra stress she is sending your way. If you could find a non-fussing way to show her how much your father returning with high sugar levels stresses you out, you might find more cooperation there too.

Let www.diabetes.org be your friend, here. It is a terrific resource for explanations and advice, including on all aspects of living and eating well with diabetes. Have a good browse around it and download anything you think you can get your sister to read.

The thing is, at heart I sort of agree with her. There is little point in prolonging life if all you get in return for your abstinence is a stick of celery and an extra three months in the nursing home. But I'm sure you just as much agree that the focus needs to be on quality of life, rather than longevity for its own sake, and that's why you go to all the trouble you do.

What I couldn't take, and I think you did well not to poke her in the eye, is that piece of wilful ignorance about how his blood sugars mysteriously rocket after cake. You are only entitled to ignore the rules if you take the trouble to understand them in the first place, and perhaps that is the point to drive home. But don't tell her about food. Tell her to get herself informed.

Just a thought - is she secretly thinking you only live once, or is she bad at giving orders?

Unless he is severely cognitively impaired it really is all on him, he doesn't need to eat cake (or any other goodies your sister brings), he is free to say no or to limit himself to a small indulgence that shouldn't cause any permanent damage to his overall diet.