Like others, I think there are 2 issues here. Most importantly is how a 5 year old will cope with separation. Two weeks, could seem as if he’d been abandoned in his little mind. I’ve had DGS1 for numerous single sleepovers, but when I had him for 4 days when DD1 was ill, he was in floods of tears on his last afternoon, begging to go home, as his Mummy would be missing him. (He was 4). It was heartbreaking and I gave in and took him to visit. Luckily with her DH’s shift pattern, I could leave him there.
The other issue is your DH’s health and in this instance, I feel should come first over your DS’s ‘want’ for a long haul holiday. DGS2 is 2 and has been with his parents to New York on holiday twice, so I think your DS (and DinL) should really get their brains into think mode!
I know it will be difficult to refuse, so get your DH up to speed and ready for a potential fallout - your son does sound a little unreasonable. This is a child, not a pet to be left.