From your post, I assume you have very little to do with your mum and DA, now that they are irksome elder ladies. This lunch may not be the best setting to teach your son that you dont cast aside elder relatives that have loved you. Maybe use the rest of the year for that? Maybe pick up these two elderly ladies for a smaller event just with your family during Christmas rather than the grand family affair? That would not bee too much, surely?
That way your dh can pick up mum while you cook, etc?
By the way, your sister, have most likely made this decision from having intimate knowledge of your mum and DA, that you may not have. I bet you dont know what it is like to cook with a demented old mum around, who insists that she knows how it is done, and dont realize that she doesnt. And he is most put out that she cant boss you around, after all she is your mum and knows best. And who decides to set the table, and see nothing wrong in what she has done, but you do, and you will be loathe to change things, as this will hurt her.
Also, who will change her nappy?
What if she is scared during the journey? Not able to make sense of the lights she sees on the motorway, the speed of the cars? Gets car sick? Needs the toilet and is too embarrassed to say?
Looking after somebody with dementia is like looking after a wilfull toddler, but with the age and experience, and demand to authority of a grown up, and with absolutely no self insight.