you are probably looking at an expression... either an expression to link the position to the parent's position and avoid using straight parenting; or an expression to modify the scale in respect to the parent's scale (essentially increase the scale as the parent's scale goes down).
if you are not having issues with any other 'parented' properties, it's probably easiest to leave the parenting in place and use an expression to affect just scale. something like this should keep the child's scale constant:
x = value*(100/parent.scale);
y = value*(100/parent.scale);
just copy and paste that into the child's scale expression field (to enable expressions for a property, select it and choose animation>add expression).
While waiting for my question premoderation, recalled basic math and came up with the similar expression after messing with stupid copying of parent scaling values and inverse it on the child object composition (but that wasn't so elegant and I still had to tweek every single child if I change parent values).