It's a bit difficult to work out exactly what's going on from your description, but it seems obvious things aren't working well.
Your DH needs a to be equally responsible for the childcare and housework etc, and it's clear he isn't being.
But your current plan is basically crazy and obviously unworkable. Is he on board with it? Because he also needs to be equally responsible for coming up with a workable plan, and if he WAS, he's have the right to criticise it.
I think you need to sit down TOGETHER and agree you are BOTH going to work out how you are going to manage things, and share the burden FAIRLY.
Some suggestions:
Firstly,
You're using all your annual leave. What about his, is is going on holiday alone this year? Why not instead take whole alternate days off? And btw, if you WFH, on your days, GET OUT THE HOUSE, or he'll lean on you. And when you get home at the end of his day to look after the DC, tell him the house isn't tIdy enough!
In his days he has your DC. If he hasn't booked it off, then I guess he's going to be WFH, taking them to the office, or looking for emergency child care (which isn't you).
I know some people are conveniently terrible at admin. If you have to, hold your nose and sit down with him and book his days off, if possible. Or don't, and just leave him to pick up the pieces.
(I also suspect he could arrange leave at short notice, if he really had to. People have family emergencies all the time, there's no reason why this has to fall to the woman.)
Secondly,
It's absolutely bonkers to take annual leave and try to do a full days work in half the time.
But you've given a good reason for why you want to do this. Again, is your DH on board with this? He needs to be. If you don't agree on this, you won't make it work.
It sounds like it's important to you, for your sense of duty but also for your career, to not let leave your employer short staffed.
So the rational answer to that is NOT take (as much) annual leave right now.
If this is the decision of BOTH of you, then obviously your DH is going to be doing the child care. Or you BOTH need to find childcare.
Does your DH share responsibility for childcare choice, or does that all fall on you too? Do you exercise veto on childcare choices, or is it truly a shared descion?
You need to BOTH make a plan that works for BOTH of you.
You can't carry on like this.