OP you sound like a whiny princess...
Your OP works full time. He isn't taking from your family - he is working for them, and getting paid for his work.
£20,000 a year isn't a professional salary, obviously, but neither is it living on the bread line either. I would have suggested perhaps not having 3 children, if you wanted to live a more affluent lifestyle 
You seem very possessive about what constitutes your money, as opposed to his money. Have you ever heard of the concept of Family Money by any chance...? Though, of course your money, isn't your money is it, really...it's actually just handouts from your family.
As for housework...it sounds like he does do some, but he doesn't do it to your standards? At least, he's prepared to do it. Stop being a martyr, and lower your standards a little bit (and see if he can raise his a little bit).
When I had 2 DDs under the age of 2, I saw 'running the house & taking care of them during the day' as my job. I no more expected DH to come home and start hoovering, than he expected me to march into his offices and start filing...
Occasionally, if I was really snowed under he would lend a hand.