Find out when each person present last saw or spoke to Smith alive. Where was each person present between the hours of 2am and 3am? Where were they at the time they heard Barbara scream? In what order did the people present come to the room to hear the scream?
It's interesting to know if any of the people present had a weapon. Logically, someone who is not guilty of a crime but has a weapon on them will tell about it to help the investigation. And the one who hides it is most likely the killer.
Try to find out who among those present heard the shots or at least some noise at night. It is unlikely that they were all asleep.
It is obvious to you that this family is hiding their dirty secrets.
Clearly, you will have to not only interrogate but also search the rooms of all the residents in this mansion. Meanwhile, try to find out which of them lived in the neighbouring rooms with the victim's bedroom.
The victim was found by his mistress, according to her testimony. And where was she at the time Smith was shot? After all, it happened in the dead of night. And didn't she do it herself?
The fact that Jacques-Jacques spent the night in the house on that particular night seems suspicious to you. He's a good shot, always carries a gun with him. Was he being framed? Or maybe he couldn't help himself and took revenge on his former friend for his betrayal?
You've looked around the house and your attention was drawn to the awards that one of the family members had won in a shooting competition. Try to find out which of the family members they belonged to.