Here are some ideas. You can choose any that you like,
and ignore the rest.
-- Do two things at once much of the time: for example,
reciting nursery rhymes to your child while hanging up
laundry.
-- I agree: David Allen said in "Getting Things Done"
that some things, like "eat lunch", don't need to be
written in any system; you just do them. Stuff like
"Do a load of laundry" can be in this category.
-- Use physical things as reminders. For example, you can
store a bottle of vitamins beside, in front of or taped
onto a breakfast cereal box, to remind you to take it
every morning. No need to write anything in a paper or
computer system.
-- if you have many things of about the same importance,
you don't need to write them down; you can just start
doing one of them.
-- cut down on housework, e.g. 1 plate per person per meal;
put most dishes in basement
-- involve child in housework -- great to develop lifelong habits
-- delegate (friends, extended family, hired help,
volunteers, spouse, child, share housework with other parents
while your children play together)
-- I agree with Ellobogrande that the GTD projects would
have actions to set up your routines. So instead of "do laundry"
you could have an action like "move toy storage to near
washing machine" (so that you'll often be near there and
will naturally tend to take a moment to start up a load etc.)
That would be something you do once to help set up a routine
which is done many times; the routine itself doesn't need to
appear in your system.
-- You can create routines, which could be checklists of
things to do in a certain order which you might post on the
wall in the rooms where you do them. Routines are easier
for the human mind to grasp if they have about 2 to 5 steps;
any more steps than that and you can group some steps into
smaller routines, name these routines and list them in the bigger routine.
For example, "eat lunch" might appear as one item in one
routine, but then in the kitchen you could have another list
to do when you eat lunch, "wash hands ..."
When creating routines, you can group together actions that
are to be done equally often; take about the same length of time;
can be done in the same room; require similar moods or postures;
have similar purposes, or start with the same letter or otherwise
tend to get connected in your mind somehow. Think about how
you and your child will be feeling; for example, people are grumpier
before naptime or mealtime. You can design routines that work well,
post lists for them, memorize them and make them habitual.
-- I agree, 10 hours is too long for weekly review. You can
look at the main categories of things you do during weekly review
and see whether some of those can be skipped altogether, or
done less often (e.g. once a month), or done in a summarized
way, or done during another activity, for example just thinking
about something while cooking rather than writing anything down,
or only writing your summarized thoughts later.
"Project review" might not mean looking in detail at a
project but could be just going over a one-page list of the main steps in
the project and quickly checking off which ones are done yet, to give
you an idea of how far along you are.
Keep in mind your true priorities, e.g. "people before things".
Just suggestions; again, use any you like and set the rest aside.