So, "llevar a trabajar" and "llevar al trabajo" are indeed different expressions, and not simply regional differences. They both mean almost the same thing, and translate directly to English in both cases. That said, I'll provide the direct translations to English and I think from there, you'll have a perfect understanding.
llevar a trabajar
infinitive + preposition + infinitive
in English we would say : to take to work
This might seem strange, because in English we omit the extra preposition "a", because as you know, English does not have prepositions already "built-in" like Spanish does.
llevar al trabajo
infinitive + preposition and contracted article (el) + noun
in English we would say: to take to the job/ to take to the work (although we don't say this in English)
Elba F.
spelling correction: is trabajo (last sentence)12/17/19