I would advise OP not to "correct" the kids' grammar - they've quite correctly recognised the basic principle of how ditransitive verbs work, and contrary to OP's assumption, there's no generally-applicable "grammatical rule" saying you can't use pronouns for both objects in such contexts.
Take for example, demonstrative and indefinite pronouns (this, that, these, those, and some, all, both, each, etc.)...
I'll show him this
You can ask him that
Give me some
...are all perfectly normal English. It might be a little contrived, but grammatically speaking there's nothing wrong with "I'll ask this that" - for example, while pointing to a computer running Google (this) with some particular question in mind (that).