Make an invisible sprite the size of the car (or a bit bigger for better touch control).
Add Drag & drop behavior to this sprite. When the sprite Is Dragging, set the car to sprite position, but only if the sprite is not overlapping walls.
You can pin two invisible sprites together - a bigger one for dragging and a smaller for overlapping checks.
Also I think you should disable Physics on the car while it's being pulled. Re-enable it when it's released.