HBP The memory in the cave... is Snape's.

[merpsiren]

No: HPFGUIDX 138047

Okay here are more of my explanation...

Would Voldemort really trust ANYONE whose family he had murdered
right before that person's eyes?

My take on this...

Voldemort demands sacrifices and punishes his Death Eaters without
consideration of what the DE may think of him in return.  Voldemort
expects everyone will fear him and that he can control their behavior
and actions by this power of fear.  So, if he killed Snape's family
and "spared" Snape's life, Voldemort would see himself as showing
mercy and expect Snape to learn that further disloyalty will be
punished with Snape's life.  Voldemort would believe this to be a
strong enough threat to keep Snape in line since death is what
Voldemort fears for himself.  

Voldemort thinks nothing of asking the Malfoy's to allow Draco to take
his place as a Death Eater.  Narcissa recognizes that Draco is being
set up as a punishment for the actions of Lucius
 and yet Voldemort
doesn't fear that this request will push the Malfoys away from him,
but demands that they make the sacrifice that is expected of them.  

Bellatrix Lestrange declares in the chapter "Spinner's End" that she
would be proud to offer up her sons (if she had any) to the service of
the Dark Lord.  

Kris