The to before a plain-form verb is generally called an “infinitive marker” rather than a preposition, because it doesn't signify direction or location as canonical prepositions do. The distinction is perhaps clearer in this pair:
Josie is going to the mall.
Josie is going to drive to the mall.
In Josie drove to relax, however, the to doesn't really mark what follows as an infinitive. It signifies “in order to” or “so that she might”. I think your source is wrong in saying that this is not a prepositional use.
Furthermore, there are experts who scoff at the notion that the “infinitive marker” is somehow different from a preposition—they say it is merely a particular use of the ordinary preposition.
What this shows is that the whole notion of “parts of speech” or “word classes“, while useful in many cases, breaks down in others, particularly with the
‘function words’ which have a very broad and unpredictable range of uses and “meanings”.
Systems of classification are valuable teaching tools. They are “handles” which help you grasp what is going on in a sentence. And as a learner, you have to master whatever system of classification your particular teacher employs, or you will fail your exams! —but don’t imagine that the system actually represents the facts. When the handle doesn’t help you understand, let go of the handle.