parents and grandparents might show their children...

[sunsunmoon]

"Can you think of some ways that parents and grandparents might show their children that they value education?"
(From Parental Involvement in School - Helping Children Succeed in School - University of Illinois Extension)

1. Is children correct?
2. Wouldn't children/grandchildren be correct?

Could you please answer these questions? I would appreciate it if you could add some information.

[Bennevis]

"children and grandchildren" would surely make it fair.

[Tdol]

"children and grandchildren" would surely make it fair.

It would, but I think many people would read the sentence without thinking that, so I wouldn't say the text is incorrect.

[Barb_D]

If you think of "their children" as "the children in their lives" as opposed to "their direct offspring" it works just fine as is. Adding "and grandchildren" interrupts the flow of the sentence.