first came sophia and her parents. her mother died and so her father remarried. later, her father ditched leaving a wife and two daughters behind. once lydia reached a certain age her mother handed lydia off to sophia to raise and then had another. this girl will be in no way related to sophia and be the half-sister of lydia.
she would have been the loved child. lydia rarely saw her mother and sophia basically raised lydia and stayed out of the way. her mother would have probably spoiled her to no end, but that is up to you. her mother did own a tailoring/boutique and taught sophia to work there. she could have taught her other daughter as well.
she doesn't have to have the last name bayley. that is totally optional. maybe her mother remarried or changed her last name. a ghibli character for the spirit is strongly recommended. mainly, because both sophia and lydia are ghibli females. her mother would have been asian so that is also recommended. though, her father is completely open to you and can be any race you want. again, if you have any questions just message me or meggles.