I've worked from home for four years now. We have a 6-year-old. And she has been taught not to bother daddy when the office door is closed.
If she comes up to bring me food, she is quiet coming in, and quiet going out.
As far as network interruptions, I have two Internet connections coming into the house, and my router fails over when the primary connection goes down.
Every single last issue you mentioned is solvable. If you're going to work from home long-term, then buy equipment that works for you.
In my case, I have a desk that raises and lowers, and my display is mounted on a VESA arm so that I can alternate between sitting and walking (I have a treadmill as well. You need to keep healthy!)