Perhaps her "missing" brother had a soulblade?
The man who had a shardplate and shardblade that Kaladin killed was Veden, the same as Shallan, and that happened a nearly year ago, Nan Helaran vanish "over a year ago" and their father had proclaimed him dead...
I'm pretty sure Helaran wasn't there that night, but he could have come back that night, Nan Balat clearly believes he is dead, but Shallan doesn't mention it beyond her father's comment.
Right now I think Shallan killed her father with shardblade slash across the chest that cut through the soulcaster. Which still doesn't tell us where the shardblade came from, why they can't sell it to pay off their debts, or whether that body that was she was drawing that was bleeding was their father or someone else(it would take a 2nd blow after death to draw blood with a shardblade), why Nan Balat had a horribly broken leg and was otherwise bruised, or why she killed her father. Besides her father generally being a jerk.
Yeah, we haven't gotten a lot to work with so far.