It sounds like your mom is referring to coupes. Originally intended for champagne, they evolved into cocktail glasses. I recommend something around 6 oz. If the links aren't what you're looking for, simply search the interwebs for "cocktail coupes".

Modern Coupe Cocktail Glasses

REAWOW Champagne Coupe

Vintage Art Deco Coupe

Rudyard Kipling "Pegu Club" Cocktail Coupe