I’ve answered this question, How one can distinguish between the usage of "gern" (or "gerne" for this matter) as "gladly" and as "like to"?, in the Duolinguo thread for the sentence
Wir würden gerne Ihre Wohnung durchsuchen
which is translated there as
We would like to search your apartment.
but my question remains unanswered.
My question arised because, in Duolinguo, until this question was put to translation, the site uses gern(e) mostly as gladly or like(ing), as in Ich höre gern(e) Musik (I listen gladly to music, or, I like listening to music). On the other hand, we have Wir würden gern(e) Ihre Wohnung durchsuchen (We would like to search your apartment, in oposition to Wir würden Ihre Wohnung durchsuchen, as We would search you apartment).
I don’t know if it is a translation problem, something about the conjunctive II that I haven’t grasped yet, or that I’m just too limited to get the German subtleties, but to me there is a difference to both meanings, one being doing something gladly, or with pleasure (I like to), and the other as a polite form for asking something (I would like to), both using the word gern(e) in German. Anyway, I would apreciate immensely your answers.