How old are your kids? I've got a 3 and a 0 year old at home (with a nanny) and even on a separate floor, the chaos is making me want a regular office job again after 5 years working from home.
I'd just close the door to my office put my headphones on (either with or without music) and get to work. Having the kids there was never an issue for me and it was nice being able to eat lunch with the kids some days.
Don't give up on working from home. Look up coworking space near your home. Or ask around to borrow a cubicle or a desk from a firm nearby.
I am trying to help my wife as I can but work needs to be done first, unless goes for life.
I get to be home throughout the day as much as I want to be, I can be home in a moment's notice. But more importantly I can concentrate or take a phone call without the crashes, cries, and screams. I couldn't get ANYTHING done from home if I tried. Maybe when they're older/in school. Until then it's $800/mo well spent.
I wouldn't trade my current situation for an office job, it's the best setup I've ever had and the whole family is a lot happier since I switched to this- but it would be a different ballgame if I was home like you. I couldn't do it, I'd go crazy.