Well your DH sounds like a joy!
I can't say I've been through exactly the same thing but...
My 3rd was not part of my plans. DH (who was responsible for contraception at the time) was delighted. I cried like someone had died. Didn't have the energy, Didn't want to be pregnant again (does not agree with me), Didn't have enough patience (I find it decreases exponentially with each child).
DC3 is now 5 months old, I had 3 babies in 4 years. I am tired cos we've hit the 4 month sleep regression but my god is she the most amazing tiny human! She is such a smiley sweetheart and life wouldnt have been the same without her.
The relationship between siblings is also something truly magical and will melt your heart.
It is a bit more work to have more than 1, but once you realise that you cannot keep everyone happy at the same time all the time the pressure eases a bit.
As for yhe dogs. Totally understand, DH wanted a dog. I was reluctant (he works away, so walking would have often been my job which would have been hectic). Funnily enough he backed off that particular wish when he knocked me up. And it'll be a bloody while before it'll even be contemplated.
As for the housework... seriously fuck it. Do enough so that its safe/hygenic and the rest can sod off. If he wants a clean house AND dogs AJD multiple children then let him do it or let him pay for cleaners. Trying to clean a house with toddlers/dogs is like trying to brush your teeth while eating a packet of oreos.
If it helps, I hated pregnancy and it made me feel crap. So I always have had much more energy after the baby arrives.
You are going to be fine. But DH needs to buck his act up or you should take him up on his offer and move out.