any ideas? It's for use in an English Language class I teach.
Among it's meanings, drive has always also had the meaning of forcing, pushing (the cattle, for example, or even some abstract thing).
Regarding the contruction itself, in which the action results in the object becoming changed in some way, it's called adjectival resultative. It is typical of Germanic languages (as opposed to Romance languages) and English features it abundantly. She beat him black-and-blue. They robbed us poor. I shot him dead.
Drove her mad can be found at least as early as 1728 in Augusta Triumphans: Or, The Way to Make London the Most Flourishing City in the Universe by Daniel Defoe:
And drives me mad from 1730 in Thomas Walker's play, The fate of villany: A play. As it is acted by the company of comedians, at the Theatre in Goodmans-Fields: