When you consistently give him full responsibility of the kids he will become more competent and they will connect and learn to enjoy time together. Go to a friends/relatives for a day. Lock yourself in the bedroom for a nap on a Saturday. Making yourself permanently available is a choice. You are not passive in this. It’s not about ‘blame’ or ‘fault’. It’s about responsibility. Yes he’s rubbish, but you can’t change his actions, you can only change your own and hope that it has an effect on his behavior, which is why everyone is focusing on what you can do.
You came here to normalize your terrible home dynamic and seek comfort from knowing others suffer in this same way, because that is less uncomfortable than looking inwards and examining your own part in this. There’s a tonne of compassion and sympathy on this thread, but as PP say, people here aren’t willing to normalize the oppression of women. You tell yourself you are doing all the right things by over contributing and are too defensive to recognize your role in de-skilling your DH and enabling his behavior.
My guess is that at some point in your childhood, you were let down, perhaps felt powerless and learned to cope however you could - not your fault, you were a child. You formed tendencies to be controlling, defensive and avoidant - patterns are no longer serving you but they will pervade until you are willing to reflect and forgive yourself.
The only thing you can change is yourself and your reactions.
If you feel attacked, it may feel challenging to hear what another person has to say while keeping an open mind. Instead, your first impulse may be to defend yourself, or you may try to turn the tables by pointing out flaws in the other person's behavior. By the end of the conversation, it is possible that no one feels heard and a misunderstanding could have occurred.
Tough conversations happen and criticism can feel painful when it comes from the people you feel closest to and even when someone has positive intentions. Becoming defensive is a common reaction to have when you feel like you are being attacked or have no power in a conversation. A defensive reaction may keep you closed off from building supportive relationships with someone else. Learning to spot when you and others act with defensiveness may be valuable in learning to have better conversations that result in solutions instead of circular arguments.
https://www.psychologytoday.com/gb/blog/insight-is-2020/202109/why-some-people-are-so-defensive?amp
This podcast is very good for listening to, whilst you lock the door, sort laundry and tell your family you are unavailable for an hour:
Self-Care for Extremely Busy Women
https://open.spotify.com/episode/1IQ1DGxa8tDXgTmJGzeW89?si=rAh_syVJQ4e6_PTJXGBR7Q
Your kids do as you do, not as you say, so what will you model to them?
Good luck!