No. You wouldn't have to cover all childcare because a. three of the kids are bloody HIS!!!! and b. he would have to contribute to childcare and everything else for HIS fourth child.
I would strongly, strongly suggest kicking him out, as everyone else is saying. Even if it is only temporary, in order to bring hom to him just how bloody cushy he has it!
Home provided.
Wraparound home-making provided (second adult, second car, cooking laundry bloody everything covered)
Some one else constantly picking up the pieces/bills/late stuff.
He really thinks he does most of the household stuff and childcare. It's insanity. Yes. So separate the households and let him EXPERIENCE what 'doing most of it' actually means.
Then you can really talk.
I think you'll very soon get used to not having him around though.
There is so much wrong here - so many things he clearly doesn't even factor in to your daily lives - for example, you don't need a six seater, do you? YOU bought one to facilitate HIS CHILDCARE RESPONSIBILITIES! So for example, you could sell that car and buy the car you'd need for you and the baby, lower fuel costs, etc. So many things like that - you say you'd need to be 100% responsbile if he went but factor in how much less you'd actually have to do...
Separate, if only to hold up a mirror so that he can see clearly. Get him out. Then give it six months and see if you love him and miss him, or whether you breathe a massive sigh of relief.