I'm sorry things are crap. Personally I would reduce conversations to a need to know basis, very minimal and factual. If he doesn't want to look after her, you can't make him, it's unfair but eventually she will see he's a twat. If she's sick, you need to look after her, that's the way it is.
I know you must be knackered but can you remark when the kids are in bed tonight?
Big hugs x