My dad is 81, lives alone and forgets things. His driver's license expired and his vehicle needs repairs but he acts like there's no issue.

First of all, tell your sister to stop making him food that just gets thrown away. Stock up his house with frozen meals, mac and cheese, anything he can prepare easily. Cold cereal if that's all that he can make himself. If he complains, ask him what he'd like, and make it clear that if he doesn't eat what he has requested, there will be nothing more prepared for him. He can order out. As long are there are things he CAN eat, he won't starve.

Call the local police and tell them dad is driving with no license. If his car needs repairs, it will eventually break down. Don't help him get it fixed, or to buy a new one.

Does he have a landline? Can he get one? Take the mobile phone away if he doesn't/can't use it.

Stop trying to get him to "listen" or "be reasonable". He can't. Stop trying to get him to do things he doesn't want to do. Only do what he asks, that makes sense. You may be at the point of stepping back and letting the chips fall, whether that be a fall or medical emergency. We have gotten to that point, as reasonable suggestions are dismissed.

Good luck!

Stubborndad, your profile says your dad has dementia/ALZ. So, he is not stubborn, argumentative or refusing...he has dementia, cognitive decline, confusion, short term memory loss...and diabetes (which doesn't play well with short-term memory loss!) There is no way to reason or logic him into compliance on anything, so please save your energies on helping him in wiser ways.

My MIL was living by herself for the first time when her husband went into LTC. We were stocking her fridge with nutritious meals, spending lots on groceries, frozen, microwaveable, convenient meals for her, etc. We discovered food rotting in her fridge and no signs she was eating anything...because she wasn't. No matter how "easy" the meal was to prep, she wasn't eating anything. She wasn't remembering that she hadn't eaten. At that point she had to go into AL. You may be at this juncture with your dad. Who is making sure his diabetes is under control?

At this point your options are:
1) your sister visits him every day, multiple times to make sure he's eating and his diabetes is under control
2) someone lives with him full-time to be his caregiver
3) you hire in-home help from an agency part time
4) you transition him to AL

FYI my MIL had forgotten how to use the microwave, stove and oven as well. She was having fender benders with her van. Unfortunately, it no longer matters what your dad wants -- he's no longer rational enough to make good decisions in his best interest. Whatever you do, you must change how you approach him since he's not just an obstinate old guy, but someone with decline who will get worse and worse. If right now he hasn't assigned someone as durable PoA, then in order to legally manage his affairs and guide his care and make choices for him you will need to pursue guardianship of him through the courts. This can cost several thousands of dollars requiring an attorney and will force you to prove his incompetence before a judge.

If you don't pursue guardianship you won't legally be able to make him do anything in his own best interests, you will need to call APS and wait for the county to pursue it.

I'm sorry I hope I'm not overwhelming you with this information but I think it's critical for families to know the full trajectory of possibilities of how things can go so that you have the most choices at the optimum times.

Also, please remove his car and tell him it's in the shop. My uncle killed his own wife in an accident because none of his children took his car when they had the chance. He won't remember his license is expired and even if you call the police when he gets in the car, it is morally wrong to allow him on the streets at at. Sell his car and cancel his insurance and put the money towards his needs. Don't become his chauffeur but find other ways to get him places, like county ride services. If he doesn't have a lot of assets, you can call social services to give him an in-home assessment to see if he qualifies for any type of in-home care.

You will also need to discretely protect his sensitive information (mobile number, SSN, bank info, etc) so that he isn't the victim of the many scammers...especially since he uses the internet.

He won't like any of the changes you are about to make, so just keep reminding yourselves it is all in his best interests and to keep the chaos in check. It is also for the sanity of his family. I wish you all the best moving forward and much peace in your hearts!

Geaton777 has a very good answer but I would think the move should be to Memory Care rather than AL.
This sounds like a man that would leave the facility at any given opportunity.
Since he refuses to go to any facility (and I doubt he has seen any to make up his mind about them) he would have to be declared incompetent and family would have to make the placement.
A visit to an Elder Care Attorney might be the wise thing to do. It is possible that he will have to be appointed a Guardian. (this could be a family member or a court appointed one. If no family wishes to become Guardian then the family will have no say in his future care or where he is placed.)

Unfortunately because of my dad's stubborness, I was told by my attorney that something would probably need to 'happen' before we could get dad to move. Removing a stubborn, ornery 90-plus year old man from his home is not so easy. He would only have gone kicking and screaming. As it was, he became dehydrated last fall and we were able to get the hospital to not release him to his house but only to AL. He was not ready for memory care at the time. And as a new chapter now, with Covid keeping him cooped up in his room for so long, his mobility is pretty much gone and he is confined to a wheelchair because he could not be out and about. It's sad. An indirect result of Covid.