Cripes....are you still debating this, winky?
Yes, read your 2nd paragraph and, of course, you should pay for your daughter whilst on holiday ....that's what parent's do, isn't it?. My wife and I have four children, and whenever we go away with any of them, or all of them, we pay for more or less everything. They may treat us to a burger every now and then.
Now in regards to paying your 'mutual agreement responsibilities' whilst your daughter is away with you, I have said before, and repeat that, in my opinion, if I were you, I would leave it as it is, as you mentioned in your last paragraph and I quote:
"We hate the sight of each other so communication is a definite nono."
It will only make matters worse and who knows what else....is it worth it?
Do the right thing, winky......and enjoy your holiday with your daughter, when you go. ☺
( We're packing for Las Vegas as we speak )