OK, I totally get where you are and why you are peed off with him.
I'm in kind of the same space, although the actual day to day issues are different, the symptoms and outcomes are the same.
It's early days for me, but I'll give you the advice I was given, and I'm hoping you can do something with it too.
Firstly: He IS who he is, you can't expect him to change his nature. Men don't do that. We can't take them on and then train/change them, we all know that really never ever works.
You didn't notice his not stepping up to the plate until you had DC, because you didn't really need him to step up until then.
You are a person with high expectations of yourself and of others, whether you you know it or not, you expected a certain something from him, a bare minimum. He told you he wasn't that kind of person, you heard him, but you didn't really believe him in your head.
To be utterly simplistic about this, you have at worst, got 2 options.
Option One, to let it all go and leave him/ask him to leave etc
Option Two: Deal with it and learn to work with it.
Before I get lightly toasted along the lines of Where's your 1950's time machine LMHF???
He does love you, he does love the family, he does want to stay together. The problem is that YOU feel let down, and he probably knows you feel this way and rather than bucking him out of it, it's making him retreat into himself, which only serves to infuriate you more... which in turn only makes him retreat further.
He has a clear difficulty in confrontation, in being able to stand up for himself when it comes to his parents, so how could anyone expect him to know what to do when thrust into the roll of DH and father.
I am NOT defending him here, I hate this as much as you, and I AM having very serious relationship issues of my own. But as I said, my dear friend who has had issues like this herself, has helped me to see things differently.
She has let go of her resentment, as I must do to mine. I must forgive him the abysmal treatment of me in his country, I must understand that the behaviour I have had to put up with are as a result of HIS inability to cope with the responsibility of fatherhood etc, and not my failings.
As my dear friend said last night, as powerless as we might feel right now, we do actually hold all the keys.
Understand him, understand why he can't deal with this, and understand also that you have to appreciate what he IS good at and what he is not. You ARE going to have to badger him into going to see his parents, but the alternative would be that you all traipse over as a family.... nightmare alert!!! Count your blessings!!
My DH doesn't do friends, doesn't do families, as soon as we are anywhere, he asks when we are leaving. he is a miserable bugger, but this is down to the fact that he can't face my family, who all know how awfully I suffered in his country, how badly HE was affected by culture shock after going back there after 20 years and being totally ill-equipped to deal with the scheisters and connivers that inhabit the land he left as a 19yo boy.
It's not that he doesn't care what you want, he cares deeply about it, it's just that he doesn't know how to give it to you.
Treat him as you wish to be treated yourself and coax him into the same. Tell him you think he's strong, he's marvellous and he's all the man you need... all that BS, but it's this that he's scared shitless about having lost. I know you don't feel it, and I know it's not true right now, but the man you are with, the father to your DC, the man you chose IS right there in front of you, you have to help HIM find himself.
I dunno if this is the silver bullet, it's what I was told last night, and it seems to be at least another way to fight the fire, it might work, it might not, but I'll never know if I don't try.
My DH adores DS, DS adores DH. DH isn't even a good dad, he does nothing spontaneously, they almost compete for my attention without either of them ever stopping to think if perhaps Mum'd fancy a cuppa, or a 5min break...
I owe my DS one more chance with DH, I owe DH one more chance to help find himself, 10 years together is a tricky time.
I may have started to ramble now, slightly hung over from last night...