The spectral character sitting in the hearth room is actually Emily Hartwood or at least shares her character model.

Theorize!

Considering Jeremy, the previous owner, was her uncle, the female specter could be her grandmother or any other female ancestor.
Also, rumour has it, that grandchildren look similar to their grandparents. I don't think there's much to this statement, but food for thoughts.

Hmm... Interesting theory, albeit one of the books in the library tells us that Howard Hartwood was the first of the Hartwoods to live in Derceto. In fact, he rebuilt the mansion himself after it had first burnt down. He was a widower when he arrived so the ghost cannot be any of Emily's relatives. The book is the one called "If Rocks Could Talk or The Story of a Louisana Plantation" [sic].

I'm not going to be the first to say it's just a model they re-used :) Is it just a coincidence there's also a picture of Emily and Jeremy (at Derceto?) in the same room?

Well, there are also stories that say that ghosts are bound to people, rather than places. If the haunted person moves to a new location, the ghost is moving along, to continue its haunt.
Of course, even this theory has its problems, considering Jeremy is dead. So the question would be, is Emily haunted by one of her ancestors and the powers of Derceto has corrupted the ghost?
If so, why is the ghost still there, when Edward is the player?

Does that mean, Emily was haunted as a child? The picture and her introduction do state, that emily must have liked her uncle. There's a picture of him and her, as you said, and the death of Jeremy was a shock for her. And since she doesn't believe of him having comitted suicide, but was killed, speaks for itself.
In any case, if Emily was haunted and liked her uncle, she must have visited quite a lot, which might have ended up trapping the ghost that followed Emily.

Or, as you said, Jeremy is a widower and the ghost is his wife.

Also, there's no statement, that Jeremy and Emily are blood-relatives. Yes, they are both called Hartwood, assuming Emily is still single. But for all we know, Jeremy's wife could have had a sister, who married Jeremy's brother. At least I can't remember Jeremy's sibling ever being mentioned. He is Emily's uncle, so he must have had a brother or a sister.
Most likley a brother, considering the wifes took their husband's family name back in the day.
Or Emily is married and her husband is called Hartwood, making it possible, that she's a blood relative of Jeremy', but his late wife and Jeremy used her as a substitute of not having children of his own.

Of course, this is just mere speculation, but where's the fun if we don't make up theories about who this ghost is?

Hmm... Yes you're right, if you're an uncle, you have a sibling. We also know Jeremy moved in from somewhere so perhaps the siblings aren't mentioned because they're far away.

Did you see this? Frederic lets us know the game had to be rushed a bit towards the end so maybe there was no time to create a new model for the ghost.

http://www.gdcvault.com/play/1015840/Classic-Game-Postmortem-Alone-in

THERE I SAID IT!

Okay, someone pointed out that the ghost isn't always Emily but sometimes it's Carnby, but I didn't find out when you get which. I swear I got Emily's ghost when playing Emily so maybe Carnby when Carnby is also true? That means it couldn't have anything to do with being related at least...

Maybe it's a Doppelgänger, then?
Acording to german folklore, you die if you see your own Doppelgänger. And the ghost is an instabnt kill, if it touches you. Also, this ghost looks different from the ghost in the ballroom. that is, if the ballroom ghosts are ghosts in the first place. But considering they are doing the same thing...

But even if the ghost switches its gender, and doesn't rule out the possibility of the ghost being a (male) relative of Emily or, more itneresting, both characters are haunted by their ancestors. It's just that Derceto's powers traps them.

I played the game as carnby and Im very certain its form is still emily.

A friend of mine spoke with the creator himself about this and... yes as I thought it's to save memory space. They made the game reuse the model that was already loaded in. The amount of stuff loaded into memory at once in this game is really low, it being from 1992.

EDIT: I think he meant it was to save effort instead of creating a completely different model from scratch, because the ghost's model is in memory distinct from Emily's or Edward's. This being the case, I don't really get it. Maybe they thought it would confuse/freak the player out seeing their own spectral image (a spectre) sitting by the fireplace.