Easiest way would be to cut down the door to suit. Best way would have been to replace the frame before the tiling happened. Do the tiles run up to the door frame or to the architrave??
Fit a con-cure unit in the house. I work for a landlord and he swears by them. You can fit them in the loft and it should solve damp issues ijn any room of the house. Other than that wall mount it in the kitchen