Opening the treasure chest for the first time will always reward you with a Red Key. If you manage to find the Faded Polaroid trinket, this can be used to immediately open the door.
If you have the Little Baggy item the skull will instead drop a Telepills, since Little Baggy replaces all cards with pills. You can use this once you have picked up The Polaroid or The Negative to return to the starting room. This skull will have a small cross on it and when blown up it will always drop a Fool tarot card. There will always be a tinted skull on the same floor as the new door. If you have any means of teleportation (for example, Teleport! or Cursed Eye when taking damage) you can use that to get out of the room once you've picked up one of the unlocking items. The problem here is that you cannot leave the Mom boss fight room through conventional means once you have entered it. This door can only be opened with The Polaroid or The Negative, which are obtained after beating Mom. Once you have beaten Mother once, there will be a new door that appears in the starting room of Depths II, Necropolis II, and Dank Depths II. Mother is the final boss of the Corpse floor, which can only be visited by opening the flesh door at the end of the Mausoleum with an assembled Knife familiar. It involves making your way to the Home floor, something that can only be accomplished once have you defeated Mother for the first time. The method for unlocking tainted characters will require a bit of skill and/or luck, depending on which character you are trying to unlock.