in this English grammar, they give five usages for between:

Between
    1. An intermediate location:  Toronto lies between Montreal and Vancouver.
    2. An intermediate time:  between Christmas and New Year's Day
    3. Intermediate in a series:  B comes between A and C in the alphabet.
    4. An intermediate amount:  between five and ten people
    5. Within a group of two:  The money was shared between two people.

That would imply to me, that "between" can not be used to describe a movement, more a location. (Accusativic rather than Ablativic in a Latin sense - says he talking rubbish)

I just felt, it was not quite right, but I know all my English teacher would laugh at me heartily. (I was consistently their worst pupil...)