With respect to kids, the clear answer is “it depends”.
There is no hard set of requirements defined in law or regs for the naturalization of children in the general case. It depends on the specific situation you envision as of the point in time when you apply. There are some specific guidelines for specific situations.
Basically, it boils down to the “ties” thing - how tied both you and they are to the country.
The only definitive published:
Anything further, you probably need to consult a lawyer since even lawyers can have at least somewhat differing experiences and opinions on the matter.
@susanayang wrote some excellent posts on this, and they should turn up in search. Some of us have debated as well.