So I tried getting them fed, making pizza which was simple, quick and easy to eat. Then I tried to get them snarling at me instead of each other, except they started to calm down. Then I tried to direct their energies into productive uses. So for mum, I had to get her to calm down and feel a bit, because she was trying to solve all her problems by Doing Things, which, given that she was so emotional, meant she wasn't always doing the right thing. For dad, that meant getting him to stop being whiny because she had been overbearing and actually support mum by doing what she told him to do. Then I pushed them into doing what they had to do, so mum went to pack while dad printed the boarding passes and reserved a car. They knew what to do and didn't need my help in any of it, except for a bit of advice here and there.
By this stage I was frazzled trying to remain unperturbed, and my attempts to manipulate them weren't going anywhere useful for them, and it looked like my parents were doing fine on their own, so I went to bed. How the hell I coped I have no idea.
This morning, I took them to catch their flight at Luton, which was at a civilised time. The traffic was light and I was in a good driving mood, so the journey was particularly quick and uneventful. They seemed to appreciate it, and I realised they weren't treating me as a child any more about the driving, since no one made much in the way of comments on my driving, which made me feel good.
Grandma's funeral is going to be on Saturday, so they will get there in plenty of time, even if things go wrong, and mum can stick her oar in on the funeral arrangements.