Thank you for saying this! I'm a full-time homeschooling parent who is also a full-time coder/manager. If distraction hit us harder than average, I would be 0% productive. And yet... I ship apps all the time.
The trick, as you say, is breaking work into small chunks. If you have to keep too much in your head, it's because you're biting off too much work at once. It's the mental equivalent of writing a 100-line method - break it into subroutines!
Also, context-switching is a skill that can be developed. We are not beholden to some sort of biological imperative to always do only one job at a time.
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