The only scenario I can imagine where Shalan's father gives the shardblade to her is: "Take this blade, kill your brother and give it back to me." That would also give Shalan a motive and explain the broken soulcaster.
It would not explain the man in a pool of blood. While the second-shardblade-strike theory has a ring to it, it still would not work since dead people don't bleed.
My favorite theory: Father beats son senseless, Shalan stabs father with conventional weapon (or steak knife), stormblade materialises, she picks it up and drops it again. Could a dropping shardblade cause the damage to the soulcaster before vaporizing?
A man in a rage has a tendency to lose outer layers of clothing so he can beat people up. I can see a very angry man throw his coat to the ground to remove the restrictions, both mentally and physically, that are implied by said coat. (Removing a physical layer allows greater freedom of movement, the coat of a nobleman also implies restraint and control. Throwing it off just makes sense.)
Shallan's father stands up from the table in a rage, charges over and attacks Nan Balat, shattering his leg and rendering him unconcious. He turns to the table, gripping the edges for a brief moment before continuing his beating of the now-unconscious boy. Shallan grabs a steaknife and stabs her father in the back. Her father dies, slumping over the table. Shardblade materializes. In shock, Shallan bends down and picks up the blade, not really realizing what she is seeing. When her mind refocuses, she realizes what she has done, leaps back and drops the blade. The blade cuts through her father's coat, lying on the ground, and shears the soulcaster.
Deep-seated guilt and emotions prevent Shallan from telling anyone about the blade.
Fast forward a year or so, and you have the Shallan of today.