I don't see any difference between the choices in pair 1.
in Pair 2, I don't understand why one would add "add the moment", unless you had in mind a temporary obligation.
Sentence b seems odd, though I can't quite say why.
In my own writing, I would not use any of your choices. Instead I would say
My children are
required to eat an apple after their meals
or
My children are
obligated to eat an apple after their meals
or, if I wanted to be very specific about the source of the requirement, I would use active, not passive
The dietary laws of my people require that my children eat an apple after their meal
or
The dietary laws of my people require my children to eat an apple after their meal