She's in her 70s, not a great driver, kids get travel sickness with her, it's 6 hours of driving.... That'd be a no from me. While lots of people in their 70s are fit and healthy and very active, there isn't an actual physical way of improving reaction time or eye sight or tiredness of someone in their 70s.
You need to point this out to your dh, he's on the defensive as he doesn't want to think of his mother like this, he only wants to see her as a abled bodied which is perfectly normal, but he needs to understand these things.
Ask him how she would feel driving that distance without getting tired, most people of younger age would get tired, this alone affects your whole thinking process and reaction time. What happens if one starts vomiting, what would your mil do? Keep driving to a safe space? How far would the next safe space be? What if there's fighting in the back, god I use to get so distracted at this, always had to pull over when the screaming started, it's just not safe to continue driving and you say it's a dangerous road, so she'll be navigating a busy road, and possibly vomiting and or fighting children all while tired.
It's just not worth it, these are your children, there's no replacing them, if anything happens it's you that has to live with it. I would not give a flying fuck who thinks what, I'd be putting my concerns forward and I would fight this decision. I bet your mil would be delighted to let you drive, she can do a shorter drive with them when they are there, like going to the shops or wherever. I know your dh has a say too but we're talking safety and lives here, it's much more of a serious decision. Of course everything could go very smoothly but why take a chance on something that has a high risk of not going smoothly, out of fear of upsetting someone's feelings.