Having kids doesn't have to be a big problem. The important thing is to have a space which is work, and make sure everyone knows that when you're in that space its like you're at the office.
I've got a three year old who is used to me working from home and doesn't cause any problems at all.
That might work for you, but every time this discussion comes up around here, there's a whole bunch of parents complaining how their spouse and kids simply will not stop disturbing them, no matter how much they try to explain that they can't do this.
I'm aware its a problem for some people, I just feel it gets overblown. Maybe those of us who find it OK are the silent majority, or maybe I'm an outlier, but I know quite a few parents who work remote and don't have any complaints about being interrupted constantly by family.
I also know of far more people who complain of being constantly interrupted by managers and noise in an open plan office. Its not like modern offices are an oasis of calm.
Or maybe your kids/family are different from other peoples'. I've seen some peoples' kids who were a complete terror and nothing could make them stay calm and quiet. Some kids are just better than others that way. You got lucky. This is a big reason I never really wanted kids; I just can't handle constant noise and commotion. I have a friend with a 7yo kid who's bouncing off the walls every time I visit; there's just no way I could live with someone like that every day. I have enough noise and commotion at work; I don't need it at home too.
And yes, open offices are horrible this way too. That's why we're having this discussion about people wanting to work from home: for many, it's a lot better than the chaos at the open-plan office at work, even if it isn't ideal. For others, it's at least as bad (kids/wife), so they either deal with the office, or they go to a coffee shop or rent a coworking space or similar.
Yeah, it's not an issue for me either. I've set clear boundaries with my family (wife and three kids five and under), and they leave me alone in my workspace. I shut and lock the door and that's it until I come out. Works really well. I wonder if those who've had problems have also had difficulty setting and credibly committing to boundaries. It may not seem like much, but if one of them tries and succeeds in getting your attention (pounding on the door, etc.) then they'll do it again. It's incredibly important that they believe that once the door is closed and locked that you're essentially not there.
My daughters love it when I work from home, so they're very supportive of my boundaries.
The thing is, that takes family members who actually respect your boundaries. I've read numerous anecdotes on discussions like this from other people who just don't have that luxury; their spouse and/or kids simply do not get it. One guy said he finally rented a little office for $500/month (or whatever), and showed his wife the bill. Then she freaked out and committed to not bother him at home, and got him to cancel his rental (though he still lost out on that 1 month's rent). And how you get some kids to respect your boundaries, I have no idea. Your kids sound great, but I've seen other kids who simply would not do this, no matter what.
I've got a three year old who is used to me working from home and doesn't cause any problems at all.