I admit that I've only recently started following this story, so it's possible that some of the following doesn't fit the facts, but... Speculation mode on.
Rather than being after someone, I think the perp/perps (equal odds on one vs two) were actually after something - probably either money or drugs. I suppose it's possible the family was involved in something, but more likely, ither they had faulty information, or they went to the wrong house.
The father hears noises at the front door and goes to see what it is. As he's trying to see out the window, the perp/perps kick the door in. The father may be knocked over/knocked backwards by the door - in any event, the perp shoots him twice. These are the gunshots the neighbor hears.
Mother may have heard this and told the daughter to hide, and may then have intentionally allowed the perps to see her in an attempt to lure them away from the daughter's hiding spot. Perhaps she ran into the bathroom? Perps drag her out of the bathroom and tie her up in a chair (the chair pictured with rope or whatever clinging to it). Perps probably start torturing the mother to get her to tell them where to find the drugs/money/whatever that they think is there. Likely they don't know there's anyone else in the house.
This goes on for 15/20 minutes. Daughter, who has been hiding, decides that she has to do something. Sneaks into parent's bedroom (or where ever) and grabs mom's phone, calls 911. (Maybe she's already tried her own phone - maybe the battery is dead? Or maybe wherever she's hiding, mom's phone is closer.) The screaming for help may be the mother.
My guess would be that at this point, either the daughter tries to help her mother/tries to make a break for it or the perps are searching the house - in any event, they realize that there's someone else in the house, and that person has undoubtedly called the police. They're out of time, they shoot the mother. Most likely the daughter has escaped and they go after her - but remotely possible that they still think the family has money/drugs/whatever and they take the daughter thinking they can either ransom her, or she can tell them where to find what they want.