This is technically just fine, and in fact is actually the grammatically correct way to say that. You will definitely not be marked down on a test or an academic paper for using
between which in that way (in fact you might be applauded).
However, the unfortunate truth is that there are cases where "grammatically correct" and "commonly used" are not the same thing. This is one of those cases.
Despite being correct, saying
between which I parked my car will likely sound awkward to most English speakers. Instead, most native speakers would probably say
which I parked my car between, even though this is not actually grammatically correct.
So, if you're looking to be correct (for example, in an academic/professional setting) the way you have phrased it is actually the right way to go. If you're speaking more informally, using the incorrect but more common
which ... between form will likely sound more natural to most people.