I don't carry on my person in the house, but we've got firearms accessible throughout, and I'd never open the door or even look through the peephole without having one if I didn't know who was on the other side.
We also have four little ones (5, 3, 2, and 10 months); we've got an adaptive plan. My wife is a homemaker, we homeschool, and I work from home. . . based on that and the kids' ages, they're never unsupervised in the house.
I keep one in my office upstairs. It's hidden in an elevated position and the office door has a key lock on it. The kids don't have access to the key, aren't aware of the firearm, and couldn't stumble upon it. It's a regular interior door that you could shoulder through in an emergency.
Our kids aren't allowed to play in our bedroom. There's a gate on the door that only the oldest is able to open. In my room is a loaded - not chambered - shotgun.
My gym bag is kept in an elevated place in the laundry room where the kids as yet aren't able to reach (even by climbing); there's a firearm there.
My wife's purse is kept on top of the china cabinet with a firearm there. The kids don't play with purses and also cannot climb - even with chairs or toys - to the top of it.
We'll of course have to adapt our plans as the kids become older and more capable, although we also intend to continue teaching them respect for firearms and how to never touch one without my wife or me present. . . up to a certain age. . . after which they'll be expected to be armed and hold a position during an emergency.
A safe is sure to be in our future, but I don't even trust the quick-access safes during an emergency. I plan to always have at least one firearm that is out of the reach of the little ones but still accessible.