Invulnerability would be pushing it. Immortality at most. As a half demon / demigod.
I was thinking more along the lines of Viv being irresistible. 

 Is there an instance where Viv is able to sway or seduce someone she shouldn't be able to, given her experience and looks (not like she is ugly, far from it, just not unnaturally, jaw dropping beautiful)? Maybe more obvious, physical traits. I don't know, like horns. 

I do think that Tara's kiss awakened "something" within Viv. At the very least Viv's curiosity. Maybe an interest in women. Perhaps her (high) sex drive inherited from mom plus by Tara's involvement with mom (?) (a spell? Close interaction with mom?) .
Anything more has yet to manifest. 

Yeah, new member. 

By the way, I'm not against supernatural stuff. Just Tara being Viv's father is on the edge of probability for me. Would the dev go as far? We suspect that Tara is a powerful demon, who can influence an entire city, either gradually or at once. So, I'm not sure.