How do we know Vin's sister was not from the same father of Vin?
We don't know. She could have been from the same father. Reen, however, had a different father, since he was her half-brother.
And why didn't Tevidan kill her? Why did he let Vin's mother live, what hold did she have over him.
Excellent question. Love? Not likely, he was a pretty cold guy, although it's possible that in the past he had more of a heart. Lust? Perhaps, although I would think she'd have to be pretty special if he preferred her favors over all the other prostitutes enough to risk his life to keep her alive.
Maybe she was simply able to escape him somehow, hide from him (with her daughters). He wouldn't have wanted to get help from very many of the fellow obligators or Inquisitors, at least not once he'd already failed to prevent her from bearing his daughter(s).
Maybe he just didn't believe very strongly in TLR's restrictions on breeding. Maybe he was just careless, didn't realize he had impregnated her, and didn't want to go to the bother of tracking her down to have her killed.