How to implement a multiple (AJAX) field collection with the FAPI
So, I followed the answer in the other thread Clive linked and this did the trick:

  $profile = new stdclass();
  $profile-&gt;type = 'some_profile_type'; 
  field_attach_form('profile2', $profile, $form, $form_state, LANGUAGE_NONE);


EDIT: Well, this is fixing the issue because it enables the form to use its widgets. But it remains a problem, the button part of the array is passed in form_state as a value, and I have to delete it manually...