I get the sense that this was a chaotic and not very well planned crime. To me, it feels like an out of control person on drugs. And if drugs are involved, then all reason and “does this make sense” goes out the window. As for why not use the gun on this poor little girl, that’s what I mean— he maybe didn’t know she was there, and didn’t have his gun loaded, or he had emptied the gun on the parents and was out of bullets— who knows.
A lot of shotguns (I’m going out on a limb and guessing shotgun, since neighbor described a “big” sounding gun) don’t hold many bullets. They commonly hold only 3 bullets. If the perp was panicked and wanted to get out of there, it may have seemed faster to just throw her in the car and speed off, rather than mess with killing her knowing the police were on the way.