Why is the second word i^i instead of le?
I'm guessing that i^i is the masculine form, le is the feminine form, and that it's a mixed group of children, thus requiring the masculine form.
I got this wrong with "eu îi laud pe copiii". Is a noun always nehotarat after 'pe'? I remember something about "am mers cu taxiu'"
Yes, usually nouns are not articulated when preceded by a preposition that is not "cu". I tried answering in detail here.
îi is a dative pronoun. It's presence here does not seem to make sense.
[Later added note: Don't read this comment -- it is wrong]
Unfortunately, "îi" is also the accusative third-person plural form, which is mandatory in constructs that use "pe" after the verb.
An alternative without it is "Eu laud copiii." (notice the definite article of the object)
Ah yes, you are indeed correct. Temporarily forgot. DL's tips and notes do not include "îi" in the table of accusative pronouns (well, it does, but only in its hyphenated form). Thank you kindly for the memory refresher!