Of course this is it.
He's a shit selfish husband and a shit father.
His way to avoid any childcare is to find a job that he is happy to do, that gets him the hell away from family life..
He doesn't care that you want help.
He will do nothing in the house as that would mean he might have to engage and get involved.
The leaving the house without telling you is all part of the same package.
Its not new, or difficult to understand.
He doesn't want to parent and his successful way of avoiding family life is this.
OP, dont have another child with him, it will only be worse.
He will discover cycling or golf or anything else.
These men are selfish losers.
As suggested, start taking careful note of his behaviour.
Tell him clearly that you know EXACTLY what he is doing.
He clearly doesn't want family life.
Give him the opportunity to separate and at least you can watch his expression when you say we can split childcare 50/50..... watch him balk.
Men like him wouldn't take a child more than an afternoon a fortnight.
OP, this is your life, he won't change.
Start looking after yourself and thinking about your future.
If you can bear to have sex with such a loser, for goodness sake don't get pregnant again.
Some women who stay and insist on having more children may find that they engage very very slightly when the children are older.
However they remain selfish losers and the children know it.