There are two issues here:
1.) Can the 14 year old become emancipated?
2.) If emancipated, can the 14 year old then obtain a mortgage?
Since the 14 year old is still looking for a job, that kind of implies that she is not an Olympic athlete or a child actress. Additionally, since the family has not moved to California yet, she is not a legal resident of that state. California is the only state which will even consider emancipating a 14 year old so emancipation is not going to be possible prior to the move AND her becoming a legal resident thereof. So, yeah, I think it's a pretty good bet that Daughter is not going to be emancipated in the foreseeable future.
I continue to maintain that the likelihood of a 14 year old (or a 15 year old, or even a 16 year old), with no credit history (of course she doesn't - she doesn't even have a job) being granted a mortgage all on her own right off the bat with no co-signer and while still in school, even with a job, is so slim as to be non-existent. In fact, I would venture to say that the instrument has not yet been invented which can measure the magnitude of slimness we are talking about here.
I have not, and will not, make any judgment about the OP's parenting skills.