As far as i can tell when you install the hydras on the LAV, according to its ammo in the model, the stat card and just plain logic it should only lose 4 stingers of the total 16 to add the hydra rocket pod. However it goes from 16 to 8.
So either the stat card and the ammo modeled in the tank is wrong, or it doesnt have the correct number of stinger ammo.
It also doesnt say anywhere what changes when you hover over the hydra rocket pod upgrade. It just says it adds hydras. Nothing about weight change, or loss of overall ammo to stingers or anything of the sorts like other modifications. I have taken a screenshot of the BMP-1 as an example, which clearly states what changes when you add the upgrade to the ATGM (although it doesnt state that the method of controlling the ATGM is changed, its still better then nothing like the hydra module on the LAV). I know that not all modifications lists what changes, but it would be nice if they all did, so you know what it does before grinding it out.