This is indeed a very good point - why touch the car at all unless if you leave it where she left it, it betrays where she really went.
There was no thus need to move it from 37SR. Her diary entry already points there; you're not going to divert suspicion away from there simply by moving the car.
So it must have been moved to disguise that she had been somewhere else. Could this somewhere else have been a different house in SR? The diary points to SR just the same, so moving the car does not help; it still looks like she went to SR. But conceivably, if parking was busy, she could have parked some way away from 37 - possibly outside or near 54. If you live there and harmed her there would you worry that she had inadvertently undermined your false trail by parking right outside? And would you move the car? I don't know. Rather than leave fingerprints or increase the chances of being seen in the car, you might be best advised to leave it where it is. You then let the police take months to connect you to her - which they may never do - and act dumb. If they find traces of her in your house, of course they did. She knew you socially.
All of which makes me think that the car was moved from the place she came to harm, and that this place was not SR.