It sounds like your mother is remembering Arthur C. Clarke’s novelette “The Road to the Sea”.

What matches

1. A great green-glass highway
   • In Clarke’s story the “Road” is a broad strip of pale-green, glass-smooth, almost indestructible material that gleams like bottle-glass in the sun.
   • It was made with techniques long since lost; people can resurface or patch it, but no one can manufacture new sections of it.

2. Magnetic / very-high-speed transport
   • Traffic moves in gyro-cars that hover a few centimetres above the surface, supported by magnetic repulsion built into the road bed.
   • Speeds of thousands of kilometres per hour are routine; the narrator notes that a trans-continental trip “takes little more than an hour”.

3. Buried under desert sand and later uncovered
   • Large stretches of the Road were lost beneath shifting sand after an earlier collapse of civilisation; in the present of the story they have been dug out and put back into service.

4. Australian setting and vivid descriptive passages
   • The whole tale takes place in the Australian desert and along its coast. Clarke lingers over red sand-hills, salt pans, sunsets over the Indian Ocean, etc., in exactly the sort of lyrical, “makes-you-want-to-go-there” way your mother recalls.

5. Written in the right period
   • “The Road to the Sea” was first published in 1950 (in the British magazine New Worlds) and reprinted many times in the 1960s and 1970s in collections such as Of Time and Stars and The Collected Stories of Arthur C. Clarke.

6. Detective / mystery frame
   • Although the story is chiefly remembered for its sense-of-wonder technology, its plot is in fact a quiet investigation: the protagonist gradually uncovers what happened to the earlier culture that built the Road, piecing clues together while travelling back and forth along it. Many readers remember it as a “mystery with SF trappings”.

If your mother looks for “The Road to the Sea” in one of Clarke’s story collections she should recognise it within a page or two—the opening paragraphs are devoted to that beautiful, bottle-green ribbon of glass running arrow-straight across the Australian desert.