Why add Vodka to Stock?
Pure alcohol is a solvent: that is: it will dissolve other chemicals more easily than water.  If you put vodka in oak barrels for long enough, it'll turn into bourbon as it will dissolve and concentrate the taste of the oak.

The same thing is happening while you're making stock:


The oils in whatever the recipe of your stock calls for will dissolve more easily in alcohol than water.
It speeds up the creation of the stock
You could use any alcohol, but if you would use Bourbon the stock would get a smoky oak taste, so by using vodka (which is 40 Vol% of alcohol in water) no extra taste gets added except what's in your stock recipe.
As alcohol has a much lower boiling point than water, the vodka will extract the oils and mostly evaporate so depending on the amount used it might be safe for children too if you follow the Halal rules but you should know a water-ethanol mixture forms an azeotrope.