Perhaps the fact that you ARE handing her pocket money exacerbates the divide?
Not sure what else to suggest, other than a prepaid credit card so it’s not so in her face?
That said, she seems determined to have a problem with anything you set up.
In terms of breakfast, it may be prudent to ASK what to get in for HER to sort herself out when she gets up, then there is no “staff”, no food being left etc, and while I travel well, muck in with anything, I would choose to eat pancakes for breakfast, and danish breakfast is even further away from British breakfasts and further from US breakfasts.
This is all so entrenched now.
If she’s there for longer, then I think a proper conversation with ALL adults to ask her if she’s happy, or would she want to go back to Denmark? She’s supposed to be there to enjoy herself, but it seems like she isn’t, so no hard feelings if she’d prefer to go back, she doesn’t have to stick it out, it’s ok to change her mind.
IF however she wants to stay and is happy to do so, then to actively muck in and stop being so dismissive of everything you’re trying to do.
FWIW, if I had to wait over half an hour for a drink in a cool box on your lap, within your reach etc, then I’d think that it was rude and mean. Wtf was your H doing driving 90mph with everyone in the car too? You could and should have got her a drink, your H could and should have slowed up so you could have passed her a drink.
Your lives sound totally over stressful, they are unsustainable at this level. I get that you have big salaries, but as you say, you don’t get to spend it, everyone and everything seems so rushed, high octane. it all seems so tense and unhealthy.
Take some time to slow down and enjoy your family, kids, marriage.