Then he's a cunt.
Reading through before this comment, yes, I'd have been fucking livid if my husband had woken me up in these circumstances. And I'd have found you not-guilty in a court after you killed him. However, it is a man thing, so didn't think it was a LTB offense.
However, this comment, him walking out, wow, just wow. This man clearly has no fucking clue that you're at burnout and frankly doesn't care. If he cared, he'd have taken DC1 out for the day, and not brought them back to the house to disturb you, little mind now leaving you to it whilst he enjoys a day off work.
When do you ever get to enjoy time off? He's getting his days off, his gym time, his full nights of sleep. He's a selfish cunt who has a wife that can deal with all of the 'women's work', so that he can continue his life at his own leisure.
His reaction to you pointing out he was wrong this morning, says a lot.
Practically speaking, is your job a career or just a job? Do you really need to work nights when your children are in childcare? I'm just confused why you're paying for nursery for two children when you go home to sleep, instead of either work in those 4 hours, dropping the nightshifts, or just drop the job altogether?
Your husband is pathetic, you've both chosen to have 3 children in quick succession and he isn't even man enough to financially provide for his family in order for his wife to raise them. I know many here do not agree with wives giving up work, but surely a 5 year career break is justified when raising children in quick succession.
As for going to stay in a hotel, I always find those comments not well thought through. It's really hard to sleep well in a hotel, with all the noise of other guests banging their doors, then housekeeping start around 6-7am, if you can afford at some point to go to a hotel, be very clear that they need to allocate you a quiet room. This is a normal request so don't feel silly asking.
Your husband needs to wake the hell up, realise you're at burnout, and taking some of the load off you. He needs to give you child-free days to sleep, and take better care of you. He should be cooking healthy meals for his family if you're too busy etc.