For the Driftwood Mines, all you have to do is wait... If you got the "Island Paradise" achievement, then the mines should be open. If, however, you're still chasing the achievement, the quest that Reginald mentioned is called "An Island Getaway". You have to escort Rusty the gambler from Bowerstone Market tavern to Driftwood in this quest.
As for the orphanage, have you checked the LAST room in the orphanage? That's where all the children are... If you are seriously that lost for directions, just enter the Orphanage. From the front door, walk up the hallway all the way to the end. There will be two doors. The one on your left will have beds in its room. The room on the right will have the children you're looking for. Even if you didn't renovate the orphanage and made it into a whorehouse instead, the children will still be there but the room's door will be locked ( I don't want to know why they're there, but if you really are that sick in the head, look for the key to that door in the room that has a bar-looking thing.)