Heavy ... look at it this way .. your W is taking the kids for 4 days, Thats it ... plane train automobile does not matter, I recall my mom stuffing us in the back of a station wagon for what seemed like 4 days (I think it was only 6 hours) for a trip.
I know when I take my S(8) back home its 1 hour in the car to the airport, 3 hour flight, another 3-4 hours in the car ... we might stay 4 days then back home .... believe me the little kids handle it WAY better than my old a$$ does. I used to drive it all the time in my military days, 18 hour drive, no more of that insanity.
I just get the vibe its about you here, I understand you are trying to shield the kiddos from the crazy MLC/WAS or whatever ... thing is she is their mom too ... My W took S up north 6-7 hour car drive, she is probably legally blind when it gets dark, but if I were to say No, that robs S of a fun memory filled trip with just him and his mom, plus just creates more things for her to dislike about me, I like you did not want her to do that trip but that was just because I felt all I loved was in that car without me, did not want me and it hurt like hell, again .. its not about us, its their journey and we are on our own.