see http://www.sleepfoundation.org/article/white-papers/how-much... for details.
Assuming that polyphasic sleep schedules are at least as effective as monophasic sleep, one such nap should be worth about an 1h20m of normal sleep. If you can fit even one in, and stick to taking it every day, it could be hugely beneficial. If you can manage to slip three of them in, you might be able to totally counteract the effects of your situation (although people seem to have trouble adopting polyphasic schedules that are designed to fit their schedule, rather than their circadian rhythm).
seriously. why?
This is what my mother-in-law has to deal with every day.
Sometimes people "[do] so much" because they have no reasonable alternatives. Being overwhelmed is a fact of life for them.
my response was directed at him, not your hypothetical single mother with a special needs child.
OK, point taken and understood. My apologies for taking your comment out-of-context.
> not your hypothetical single mother with a special needs child
It wasn't hypothetical. That's an accurate description of the life my mother-in-law leads.