There would be no need to wear both. It is the same scapular, just with differing expression. I have seen some of the small devotional scapulars with an image of Saint Dominic on them. The “regular” scapulars tend to be a bit larger, made of better material in order to last long, and unadorned with image…just as the full size scapulars worn by the friars, nuns and Sisters are without an image.
You can choose which one you prefer to normally wear between the two, if you are speaking about the first scapular you mention in distinction to the scapular the fraternity may uniformly use for investiture.
The rule makes provision for choosing among various options what you will wear as a sign of being a Lay Dominican. There might be circumstances in which you would choose a medal or pin, for example, in place of the scapular.
The large scapular of the Lay Dominican is only worn on special occasions.