What Dwight55 said is correct, for I've done some practical research on sideways movements, as well as retreating vs. going forward.
It appears that the "strong hand" is less effective when shooting at targets that are moving in a direction away from the center of the shooter's body (i.e., a right handed shooter firing at something moving in the opposite direction....or, from the shooter's view, the target moving in a "right-bound" direction).
Additionally, the muzzle climb of most handguns and rifles tend to be upward and to the left....so, if the shooter tries to make a follow-up shot on something moving to their right, they will need to correct their horizontal positioning more so than if that something was moving to their left. This is somewhat prominent in full-auto weapons, when you see the "spray" of rounds on the target going upward and to the left, at least most of the time.
Bottom line? Have your loved ones run to THEIR left and away from the shooter while YOU drop down, unholster and take aim. If you can't find cover, you might need to prone out (Give some thought to that, for when you drop down to a kneeling position, that will also act as a momentary diversion AND will cause the BG to perceive that YOU are more of a threat to him than your loved ones that are running AWAY. If you can immediately prone out and shoot, YOU will be a smaller target for the BG)
Just remember....Your loved ones need to run to THEIR left, which will be to the BG's right.