I’m kinda sad this part isn’t adressed more. Being suddenly abandoned and left in deep debt by your parents should be traumatic, but it appears to only be used as an excuse for them to move together and then forgotten.
Kei probably doesn't know what whiskers are, so it wouldn't be weird for her to think it's a moustache. And my understanding is that Japanese uses the same word for all facial hair, but is often translated as just beard.