Entropy confusion, please help!

Trying to explain entropy to kids, I find that I need some help with
understanding the concept... The second law of thermodynamics is
usually stated as "Heat (energy) flows from higher temperature
objects to lower temperature objects, until thermal equilibrium is
reached" (please correct me if I'm wrong here...), sometimes as
"in a closed system, entropy (a measure of disorder) will always
increase" and sometimes as "natural processes cause things to move
from improbable and unstable orderly states (less entropy) to probable
and stable disorderly states (more entropy)."
Now, for example, is not ice (water crystals) a "stable and
ordered" form, liquid water a a more random form, and steam the most
chaotic form, of H2O molecule "order"? I also remember reading
somewhere that "entropy is zero in an object that has no thermal
motion, such as a fictitious crystal at 0 K"...
This is where I find confusion: Since heat indeed flows from hotter to
colder objects , it seems to me that, at least in the water example,
entropy goes from higher to lower... And if "absolute zero" is
where we find the highest form of order (zero entropy), isn't
universal entropy running from maximum disorder (big bang, with its
very high temperature) towards minimum disorder (the absolute zero
"heat death" of a completely "run dowm" Universe)?
Intuitively, I think of the atoms in a white-hot piece of iron as
"moving more randomly" than does the atoms in a piece of iron that
has been in a freezer for a few days. Likewise, I think of the state of
affairs immediately following the "big bang" as a whole lot more
chaotic than the absolute thermal uniformity of a Universe that, some
time far in the distant future, has reached "absolute equilibrium"
Obviously, my thinking is flawed. Can someone please help me get this
entropy stuff straight?
Many thanks in advance,
Uno

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