@sheaprior - Did you see the jumbo sock inside the laundry machine? This should add a dialogue option with Becky, asking her about her laundry. After that it should be possible to give her the key.
@sblob -
*** spoiler ***
Getting the mirror key is a step in the process of getting the thick socks.
To get the mirror key you'll have to:
1) get the note from the thorn bush using the garden shears.
2) read the note and learn that there's a voice message on mirror Becky's phone.
3) Give real Becky the broken phone you found in the mirror bathroom, and then she'll lend you her phone. Mirror Becky will give her phone as well and it will be waiting for you on the floor in the mirror living room.
5) listen to the message on that phone. It will reveal to you the location of the mirror key.
*spoiler*
@fundurian - If you show the picture (from the photo album in the bedroom) to the sister she will give you a package. The reverse album is in the mirror package, but you'll need a knife to open it. The knife is under the sofa in the mirror study room (You'll need a working flashlight to get the knife from under the sofa).