"but how much force would it take to crack her skull like that since she was only 6 years old?"
A LOT.
To do well in pageants she would have had a certain amount of spunk and confidence. She also won the argument with her mother about what she would wear to the party, which means she had her own opinions and the ability to stand up for them.
Whether this would also mean she would resist/fight her intruder, I don't know, but she did have someone's DNA under her nails.
Not as much force as it would take to cause a similar wound in an adult.
Also, a weak person could do it if that person had enough leverage. Leverage and the mass of the object used increases force. Another child could easily do it with a swing of something like a golf club. If the child doing the swinging had enough room to swing the club so it picked up some speed, that plus the mass of the club head could do the damage.
In other words, lacking more information, we simply can't tell from the head wound how it happened. A forensic professional might be able to say from which direction the blow came and even take an educated guess as to the shape of the object that hit her. But I think exactly how it happened would remain a mystery.