So, my bit of Theorycrafting (more just musings). I don't know much about the Inanna/Ereshkigal aspect. From my VtM experience, tho', and it's connection/inspiration/etc. to the game, I DO make some assumptions, although I fully expect there's not a 1-to-1 connection. I don't think any of this really qualifies as spoiler, so....
1. There's a connection between Sire and Childe (pretty obvious), and Sharon's particular history does easily explain her behavior to Laurie now.
2. In VtM, old, early generation vamps have a LOT of power. In VtM terms, PC could quite readily be, say, 5th generation and Sharon's a good ol' 12-13th. I suspect this has slowly been dawning on her (and rapidly of late). This is the easy stuff. One could start going down the rabbit hole and muse that Sharon turned Laurie before the PC inevitably would to have another hook on him. That'd be quite consistent with VtM, but I don't think so much in this story. A cynic might suggest that she already viewed Laurie as something of a rival, and if/when PC inevitably turned her himself, she'd be a rival with a much stronger generation.
3. Calisto. Ahhhh, Calisto. My prevailing assumption is that she is quite aware of what's down in the cave and has been for awhile, and that's pretty much why she sired a childe - a fire-and-forget missile at dealing with a sticky problem. Hook him up with a damaged vamp (damaged in that Sharon seems to actually care) asw nursemaid, surround him with those who can teach him/unlock some of his power, hook him up with the Nos, who, if you're about to get in a scrum belowground, are the No. 1 clan to have at your side.
There's almost zero risk on her part. If he succeeds, it will be because he's become quite formidable, which makes for a terrific ally (and one that is bound to her). She gets rid of a problem, she (importantly) doesn't let anyone else get rid of it, which could have meant the elevation of a potential rival, and she risks pretty much nothing. If he fails, well, she's better informed about what is evidently a more serious problem than she wished. Plus, in whatever level of vamp society in which she has peers, she gains a big Smiley sticker (with gold star!) for cleaning up that serious problem.
4. Last little bit related to Callisto securing a formidable ally in her Childe PC...he'll inevitably sire vampires in turn - whom also will be of quite elevated generation. Carmen, Ivy come to mind. Carmen, in particular, would (will!) make for a fantastic vamp. That's a nifty little power base being built up. She doesn't seem like she needs it, but...if this Inanna/Ereshkigal thing goes on, she very well might.
The one rule above all I remember about VtM, was when someone asked a very well informed source what the most common mistake players make was, "They think they can win."
(sorry if this is trodding over well-covered ground)