"La gepatroj mendis po du libroj por siaj tri infanoj."

They ordered 6 in total I believe. That's what the po (each) is about.

You are right, the sentence could have both meanings. The number “tri”, however, strongly suggested the second meaning to me.

The other meaning could be unambiguously expressed by adding “Ĉiu el [la gepatroj…].”

But it's after the preposition "po".

Nouns after prepositions take the nominative case (except in a few cases related to directions).

Similarly with "multe da libroj" (nominative after preposition "da").

Language usage about “po” is a bit controversial in Esperanto. For some, the reasoning is “ĉiuj prepozicioj per si mem postulas la nominativon” (rule 8 of the 16 basic rules), so no accusative. Others consider “po” to modify only the numeral, not the noun, which preserves the accusative it would have without “po.” Both ways are considered valid.

You could say that the sentence is analyzed either as “mendis (po du libroj)” or as “mendis (po du) librojn.”

Po isn't used in the English translation

"each" is there in the English sentence.

Your sentence most readily means that they bought two books, in total, and that the three children had to share those two books.

The English "two books each" and the Esperanto po du libroj implies that the parents bought six books: two for each child.