I get what you are saying OP. My DH could have phases of this. especially the 'well I got up with DC' when actually getting up means putting them in front of a screen and going back to sleep. Not actually getting the breakfast or a drink or dressed. That all waits until I am there.
I think you need to break it down into different stages to make progress. As much as your DH SHOULD see what he's avoiding there, he probably won't.
Your DH can and should be able to deal with both kids at once. So make a plan for yourself to:
- send him out with both kids and
- you go out for yourself for a decent amount of time
figure out when it SUITS YOU to fit them into your week and then make it happen.
Seems to me part of your resentment is your DH says 'can I go for a drink with friends' and then stays out super late, when you don't get to do anything.
So start arranging things.
I started with commitments out of the house as that was clearer. So I'm going to an exercise class, or I'm going to meet my friend for dinner.
A few times over the years the thing I had arranged has fallen through - I missed my exercise class at your stage, faffing settling the baby and leaving too late. But I went out anyway, bought a magazine and a coffee sat on a bench in the park in the sunshine for the hour I'd have been at the class.
I arranged stuff that I felt best fitted with the kids and their routines. As DH was rubbish at that stuff, so I set up things where I'd go out while the baby was napping and he did the next bit when they woke. As if I left him to settle for a nap he'd miss it and then I'd pay the price that night.
I'd also start sending him out with the baby and the three year old. So for this morning what would have annoyed me is he could have taken the baby to the park too and given you a break. But you suggested he just take the three year old. Next time tell him to take them both!
The scarf thing - I get it's annoying.BUT - it does sound like he was trying to make you smile. That's a good thing.
You don't HAVE to sort it all out. Get him to help you. Or just say - hey, would you pack those bags back away please.
I think at this stage Dad's can lean into the relationship with the older one. It's nice to be wanted.
AND they can be guilty of hiding away from the tough bits of life with a baby doing 'useful' (read: easier) things with the older child, or for the house, or whatever.
Start giving him time with the baby - and GO OUT when you do, so he can figure it out himself and build that relationship (and take times when it's hard).
So also start taking out the three year old yourself and leaving the baby with DH. Some one on one time will start to rebuild that relationship too.
Lastly - maybe get some advice on the baby. Around this stage DC2, previously a champion sleeper, started waking hourly every other night. Rather than ride it out as I'd done with DC1. (which took two years and nearly broke me) I called Ann Caird at Nurturing Sleep (she was recommended on here) https://nurturingsleep.co.uk/ she was amazing and insightful and a few sessions helped me turn things right around.
My only regret is that I didn't call her with DC1!