Please explain the theme of women and children in Richard III.

I am not so sure that this question is about theme, rather
it appears to be about character, and the presentation of women and children in this
excellent play.

Clearly, the most important children in the
play are the two young princes who were so famously murdered in the Tower of London. It
is important to note how Shakespeare brings them to life and makes them very intelligent
and articulate figures. They, interestingly, are the two characters in the play who are
not fooled by Richard's character and see through his deceit. They are also very brave
and valiant in how they defy him and they likewise show that they can more than triumph
over Richard when it comes to puns, which is something that Richard uses to show his
dominance over other characters. There only weakness is their age, which renders them
intensely vulnerable to their uncle's stratagems. As such, their death appears to be
inevitable, though Shakespeare maanges to breathe life into these brothers to such an
extent that we are left with the impression that they would have been excellent kings.
To this end, it is correct to say that they are used as foils for
Richard.

Regarding women, you might want to consider the
role of a character like Margaret, who, although possessing only a minor role, seems to
be a very interesting character to focus on when we consider the presentation of women.
She is most famous for her itinerant wanderings around the castle and her curses, but
she clearly represents a kind of all-consuming yet powerless rage that she holds for
Richard and his family. This rage seems to symbolise the anger of all of Richard's
victims against his nefarious deeds. You might want to re-examine her curses that she
utters to Richard and his family in Act I, which foreshadow the rest of the play.
Likewise her character also seems to symbolise the fate of women in a patriarchal power
system. As a widow, she is left in the extremely uncomfortable position of having to
raise her begging cap to her family's murderers to survive, which is of course something
that tortures her. She is a flat character in many ways, but she is nonetheless used to
centre the rage and desire for revenge on Richard himself.