But you aren't calling their bluff, you're giving them what the want.
I completely agree with this. They know the trip is important to you, so they are trying to take it away from you. The only people who will suffer is you. They will be just as bad if you stay home. And they will have won - again.
Going against the grain. I would go. A change of scene might help.
They are 6 and 9.. testing your boundaries, the 6 year old is following the 9 year old.
For us. It was like not walking a dog. They had to get out every day and run about or they went stir crazy. Also I found that everything was easier in the open air. They had a phase where also wouldn't get in the car, wouldn't get out the car. These things go in phases. Rude - say so. Ask them if they would like you to talk to them like that? Fighting? Separate and distract. Both be on the same page. Showing them you are angry on a daily basis (and I'm not saying you are) just shows them that's the way to deal with things generally. So you have to put that to one side. Pick your battles.
Are you discussing things too much with them? Requesting? "Would you mind awfully getting in the car." or (I understand why) asking six times and then losing it and shouting at them "Get in the CAR NOW) . Its a bit like asking your MIL for permission or approval LOL. You wouldn't do that?
Try, quietly get everything ready, load the car, if they won't put on coats/ shoes.. put them in the car. No discussion. No appeals to their better nature. Its happening. We are not angry. We are just doing it. Bribes are good. I used to have a holiday party bag with fun things (identical so no squabbling) with card games, Kinder surprise, magnets, toy aeroplanes ( even 9 year olds like these). Instead of saying no then giving in to the pleas for ice cream. They get an ice cream or holiday allowance... you will be surprised at how long they spend choosing things, but also gives them a bit more of a say in things.
Telling them off all the time eventually goes in one ear and out the other, it starts to be ignored.. then you have to up the ante.. but you can't keep upping the anti. Best advice I was ever given is when they are getting more and more noisy, defiant or quarrelsome, don't join in.. start lowering your voice and try to keep calm. Set the example, even if you are not feeling it. Are other people/relatives getting over involved? Giving advice?
Take the 9 year old out on his own one on one. Buy him a treat and talk to him about his favourite things as you would a friend. No telling off. If he acts up.Just chat...ask calmly with no tone, why are you doing that? see what happens. Do the same with smaller one. Sometimes that's a way to get them really talking to you when not in a rush for school/bedtime etc... Ask what kind of holiday would you like? etc.. instead of them just saying no to everything. I think they are enjoying the power and the drama of all this. Imagine being able to stop your parents going on holiday, how powerful.
They are nearing the end of term and are probably fed up and exhausted...I found that always ramped up behaviour. Don't forget the 4.00 pm hangries. Pyjama day with plenty of food to catch up. Have a good look at things like school/friendships/activities and see if these need a new approach.
None of this works overnight by the way but its worth a shot. Have a good half term x