Depending on how long the timeframe was between the head injury and the asphyxiation they may not be able to definitively point to all of the details and timing so precisely.
If you interpret the garrote and everything else following the head injury as a cover up you are left with an extreme set of psychological hurdles for a killer to make, particularly a parent.
She did have a head injury with a severe skull fracture that apparently didn't bleed, no matter what the weapon may have been. What I'd like to know is, was her DNA on the flashlight?