So true. Before my kid was born (now 1½ years old), I optimistically thought I'll be able to work at home while baby caring, which turned out to be very naïve idea. It may work with a newborn, but definitely doesn't with a toddler.
In the UK if you apply to your company to work from home it will certainly be dependent on you having separate childcare arrangements.
You're absolutely right though.
My daughter is 16 months old. On a day when I'm looking after her on my own I might get one 45 - 90 minute chunk during the day where I could do something approximating to work (when she sleeps - though you've probably got clearing up, catching your breath and other things in there depending on the mood they've been in).
Other than that you might be able to read and reply to the odd e-mail, check the odd thing or make a quick call or two (so long as you're happy with the possibility of a child shouting in the background) but nothing that could be classified as productive - certainly don't even think about coding being something that might happen.
That all runs from 7am to 7pm. Once they've gone to bed you have to eat, clear up and get ready for the next day before you start thinking about what you want to do. On a good day where they're behaving you can clear up as you go and you're set by 7.30pm, have eaten by 8pm and you're good to go.
On a bad day you've eaten by 9pm and you're dead on your feet. Looking after young kids is full time and I will never question what stay at home mothers do with their day again.
Still wouldn't change it though - I miss having time to do the things I used to do but I'd miss her far more.
