Here, working remotely for six years. I think that it's all about home-office, if you have a unique space, called office all changed a lot if not is still your house and you feel like extra-hours.
For this six years, for one year I didn't have a spare bedroom for the office, and that was bad, I was working from the dining room and a lot of problems. (As you have now)
Now working from a spare bedroom-office, with nice desk, large 4K screen, a good chair, etc.. Highly recommend. Around network problems, I have two internet connections, one for failover with another company, all wired, so I don't need to worry about the wifi.
Around kids, I don't have it yet, but a lot of my friends said that it's about that they should understand that you're working, and for that, you should have an "office".
Regards