I haven't read the whole thread, just your posts, OP.
First off, I hope your daughter is getting better, and that somehow, you are managing to get some rest, and that both of you are able to access decent food. Thank goodness for your best friend having your other child!
I'm from NZ. My DH travels a lot for work, even more so when we lived there. I know what it's like to be the one home holding the family together, treading water while the other one is off on business travels.
Your DH is being a self absorbed lily livered chicken shit. If nothing else, he could man the fuck up and show his wife and his daughter that he gives a shit about them both, and sacrifice a tiny amount of his precious fucking beauty sleep, and face time them, to see how they are doing for himself, be sympathetic, and at least give some semblance of sorrow that he isn't there to support them both.
These are the kinds of things you don't forget, not as a spouse and co-parent, and not as a child.