This is happening to a lot of us as our relatives get older. Complicate it all with Alzheimer's (as is true in my family), and daily life, not just the holidays, gets complicated.
I'd bite the bullet this year and go to his folks' house given the time frame for decision making. Then spend the year trying to figure out how to handle next year.
I hate to point this out, but at some point our parents need their adult kids to drop by the house and assess how they are living at home. Are they able to take care of themselves? What kinds of things need to be put into place so they can stay in their homes for as long as possible. Driving may be the least of your worries. For instance, did dad go to the doctor after this illness? What was that all about?
It's a good thing MIL has stopped cooking. Many elderly people stop when they realize their memory isn't as sharp and their reflexes weaken. Cooking takes timing, measurements, etc.
Spend one of the days hanging out with them doing their normal routine. Find out who their friends are at the restaurant they eat at, etc.
Basically, it will be the best gift you can give them--a "check up" on how they are getting along.
And cook at their house. Make decorations. Go caroling. Figure out what Christmas is like there.
And don't think they are so old-fashioned! My parents don't own a computer. :)