A Mom with young children recently asked a great question about how to keep Shabbats, including Yom Kippur/Day of Atonement when you have little ones to take care of.
The simple answer: Just use some common sense.
The longer answer is this:
The truth is, a mother’s work is never done. It's impossible to for a Mom to NOT do some "work" on any Shabbat (including Yom Kippur), be they the weekly or the yearly ones - especially when she has very young children.
Life HAS to go on!
(This also means that YOU must take care of YOU. Fast on Yom Kippur, if you can, but don’t put your health and well-being in jeopardy as you spend your day taking care of your children. And by all means, do NOT make your little ones fast. Gradually introduce them to “denying themselves” as they grow older, by – for instance – not allowing them to eat certain things or denying them some video watching on Yom Kippur.)
YHWH didn't mean for any of His Shabbats to be a burden; they are to be joyful days of rest away from your normal, "income-producing" work.
Each of the yearly High Holy Day Shabbats have a special meaning, and as long as you know that and are sincerely doing them to the best of your ability, you won’t be guilty of “breaking” a Shabbat.
So, yes, it’s especially difficult for a housewife to properly keep any Shabbats – unless she has no children and can prepare her food ahead of time (on Fridays or in the days prior to a yearly High Holy Day) and leave the dishes and other housework until after the Shabbat. But, as mentioned above, with small children, life MUST go on!
Therefore, simply employ some common sense and do what you need to do on Shabbat (or High Holy Days, including the upcoming Yom Kippur). Clean up the messes, get your children fed and taken care of, play with them, let them watch some children’s videos, and REST when you can ... while remembering throughout the day to talk to YHWH and thank Him for His blessings, acknowledging that it’s Yom Kippur (or whatever the High Holy Day is at the time).
When the children get older, teach them about Shabbats and what is to be done on each of them (both weekly and yearly). Teach them to clean up their own messes to give their Mom a break, especially on Shabbat. (There's no reason why, for instance, a 10 year old can't clean up their room or their own toaster crumbs or to clear and wipe off the table after putting their dishes in the sink … ANYTHING to help the mother out and make her day’s work a little easier.)
Just remember, YHWH knows whether or not you’re trying, so give yourself a break and do the best you can – but ALWAYS BE SINCERE, because He KNOWS who is truly trying their best, and who is only “halfhearted.”
YHWH’s Shabbats and High Holy Days are hard to keep in a Torah-less world, and really, NOBODY knows exactly “how to do” them. We’re all just doing the best we can.