Both "Please take off your shoes" and "Please take your shoes off" are grammatically correct, but the first is more idiomatic than the other. And yes, verb phrases normally stick together, but they don't really have to. As another instance, we can as comfortably say "Turn off the light" as "Turn the light off." It's just that it's much easier to say the preposition right after the verb rather than make the tongue fumble for it later, particularly when the object of the verb is a long noun phrase, as in "Turn off the light at the far end of the garage." See what happens when we defer the preposition to a little later: "Turn the light off at the far end of the garage." Or to much later: "Turn the light at the far end of the garage off." Verb phrases tend to stick together for the speaker's convenience; that is, they are idiomatic or habitually spoken.
