Well you don't have to use sugar. It is there just to off-set the strong vinegar bite a bit. It only plays a very small, if any, safety role anyway. But you sure need to use a tested recipe when it comes to knowing how much vinegar unless you plan to use straight 5% vinegar.

The taste would be really off-putting to me with white vinegar and no sugar but taste is a matter of preference. If you like them that sharp and acidic then go for it. You can always add a bit of sugar after opening if they are too sharp.

Personally, given your list of ingredients I'd use the Pickled Dilled Okra recipe and sub the green tomatoes for the okra.

The problem with "Mom recipes" is that we often forget, or never knew, exactly what all was in them. She may have put sugar in when you weren't looking. ;)

Dave