AB offer "late night check-in" (Vorabend check in) at DUS for all flights (
http://www.airberlin.com/site/vorabend_check_in.php )
If BA refuse to through-check the bags (because of your family not having a BP for the ex-DUS TATL), then they should be able to reclaim their bags at DUS and then immediately go to the AB counter, check in and drop the bags for the following day's flight.