Given that this isn't V:tM, it seems pretty close, lore wise. So this may be something people are interested in.
The "drinking three times" thing (Enthralling) is sometimes performed by a Sire (the vampire-creator) to ensure the created vampire remains loyal (fanatically so) like enthralled humans (Ghouls). But it is seen as an extreme measure.
One of the tricks performed by the more immoral Sabbat (the "eviler" vampires of the V:tM setting) is to have an entire pack share blood three times (Vaulderie), thus binding them to all the members of their pack in a low-level binding (Vinculum) and breaking any other blood bindings they may have.
Specifically, each one of the three drinks increases feeling toward the supplier. Every vampire (Childe) has at least a low level bond to their creator (Sire). If Sharon warms (even more) to MC, I think I'll always be speculating if it was the act (sharing of blood) or the blood itself (creating a low level bond).