Kind of reflecting what Granny said, can't you just say you think it is important for you both to have your own space, and, to that end, in view of what happened at xxx, you are taking the dc away on your own this time as it will be more relaxing for both of you.
I think holidays with extended family can work, but it's obviously not for you and your dm at the moment. I don't know the back story, but she sounds very unhappy, and I imagine that's why you persevere, in the hope that things will get better for her? But in the process, you're putting a lot of stress on yourself.
For your self-preservation you need to take a step back, take control and say 'I'll always be here for you. This is what we're doing this time. I'm sorry if it upsets you, but it's for the best in the long run'.
The fallout won't necessarily be as bad as you fear, because at some level she must know herself that her behaviour isn't healthy.
(I know it's all much easier said than done! Good luck, and enjoy your holiday
)