OP - why don't you "let" him go, so long as he's away at least a fortnight. Then you can have a decent crack at NCSS. If it's not made a positive difference by the time he comes back, then it's time to admit it's not working for you, don't you think? Then, you go away for 3 nights and let him have a decent crack at his way.
I hear what you're saying about not enjoying going away - but most of this sounds like not enjoying going away with your family, and there's no need for it to be to somewhere new, or even far away, you could go to your parents or a friend's.
FWIW, I think NCSS can only work for text-book babies, who don't need it anyway. I've read it, even tried a couple of nights with dd3, and it was utter nonsense where she was concerned. With all of them I've done "cry it out" and they've slept through within 2-3 nights with only 1 long crying episode (though dd3 reverted several times, hence trying NCSS). So worth it over many nights of them crying a bit. NCSS did not involve no crying for us!
But clearly this is all about other issues between you. He is a parent of your dd2 too, and he loves her (I'm sure), and he has the right to have some say in how she's brought up, including how she sleeps.
Also, I can't understand why her not sleeping through would prevent you going anywhere with her? In our family, we would all go on this trip. When dds were 4y, 23m and 7m we had a trip to South Africa, to attend a wedding, and it was one of the best holidays we had. Kids are easier when you have 2 adults on call all the time, and that's how it is on holiday.
Good luck.