Oh my word!
I hope all of you that are shouting divorce and life on a park bench are just demonstrating their outrage with words and aren't even slightly serious about such suggestions.
If not I'm utterly astonished.
Heather, fair play your OH is behaving very badly, heaven only knows what's going through his head to think his behaviour is acceptable.
I personally agree with those wh have said, do not tidy up, switch off your phone, have a hot bath, a good meal and some sleep.
It's the best thing you can do for your family. You'll have enough energy to get back to the hospital and look after DD and take over from your OH, OH will have a proper look at life as the parent of a sick child in hospital and realise it's no party and when he gets home and has to tidy up will hopefully get some idea that there is work to be done by both parents of a sick child. Don't pick up the slack he's produced, but I wouldn't divorce him either. (IMO) being a parent is a learning experience, if you shield him from the harder parts of that experience he'll never know. Ideally he'd be wading in their to have the experience but he isn't and that doesn't mean it's your job to take over for him. A dirty house won't hurt anybody but being there for your daughter when she's ill (both of you) has to be the top priority whether he likes it or not.
Just to throw in another facet to this, has OH ever been in hospital as a child? What did his parents do if he was?
I just ask as when I was in hospital with DD who was 2, I was horrified that a little girl (aged between 4-6, I can't be sure as my dd was only 2 and I guess I wasn't a great judge of older childrens age) was left alone for the 2 nights I was there. Both her parents opted to leave her. When they did come in they read magazines, chatted amoungst themselves and barely said more to her than to tell her off. I don't know if that little girl will grow up and treat her children in the same way or if she'll demand to be with them, but it made me wonder.